Methods of obtaining geometry from images

ABSTRACT

In one aspect, a method of detecting at least on feature associated with a blood vessel in at least one image of at least one blood vessel using a matched filter adapted to respond to the at least one feature is provided. The method comprises applying a scale detection filter to selected voxels in the at least one image to determine a scale for the matched filter at each of the selected voxels, determining an orientation for the matched filter at each of the selected voxels, wherein determining the orientation is assisted by using the scale determined at each of the selected voxels, applying the matched filter at each of the selected voxels at the scale and the orientation determined at each of the selected voxels to obtain a filter response at each of the selected voxels, and analyzing the filter response at each of the selected voxels to determine if the respective voxel corresponds to the at least one feature.

RELATED APPLICATIONS

This application is a national stage application under 35 U.S.C. §371 ofinternational application PCT/US2009/000008 entitled “METHODS OFOBTAINING GEOMETRY FROM IMAGES,” filed on Jan. 2, 2009, which claimspriority under 35 U.S.C. §119(e) to U.S. Provisional Application Ser.No. 61/009,872 entitled “METHODS OF ANALYZING VESSEL DISTRIBUTIONS ANDUSES THEREOF,” filed on Jan. 2, 2008, and U.S. Provisional ApplicationSer. No. 61/010,080 entitled “METHODS OF ANALYZING VESSEL DISTRIBUTIONSAND USES THEREOF,” filed on Jan. 3, 2008, all of which are hereinincorporated by reference in their entirety.

FIELD OF THE INVENTION

Aspects of the present invention relate to extracting geometry from oneor more images for use in analyzing biological tubular structures fordiagnostic and therapeutic applications in animals. In particular,aspects of the invention relate to extracting geometry from images ofblood vessels to identify structural features useful for detecting,monitoring, and/or treating diseases, and/or for evaluating andvalidating new therapies.

BACKGROUND OF THE INVENTION

A wide range of imaging methods and devices are commonly used toevaluate different anatomical and physiological conditions in a varietyof medical and research environments. Tools have been developed to imagebody structures based on different physical properties. For example,X-rays, CT scans, MRIs, PET scans, IR analyses and other technologieshave been developed to obtain images of various body structures. Thesetools are routinely used for diagnostic, therapeutic, and researchapplications. Combinations of two or more different imaging techniquesare sometimes used to provide complementary information about a patient.

In conventional medical imaging, a human operator, such as a physicianor diagnostician, may visually inspect one or more images to make anassessment, such as detection of a tumor or other pathology or tootherwise characterize the internal structures of a patient. However,this process may be difficult and time consuming. For example, it may bedifficult to assess 3D biological structure by attempting to follow 2Dstructure through a series of stacked 2D images. In particular, it maybe perceptually difficult and time consuming to understand how 2Dstructure is related to 3D structure as it appears, changes in size andshape, and/or disappears in successive 2D image slices. A physician mayhave to mentally arrange hundreds or more 2D slices into a 3D picture ofthe anatomy. To further frustrate this process, when anatomicalstructure of interest is small, the structure may be difficult todiscern or it may be difficult to understand how numerous structuresrelate to a biological whole.

Furthermore, in addition to the time consuming nature of manualinspection, human visual interpretation of images has furthershortcomings. While the human visual cortex processes image informationto obtain qualitative information about structure in the image, it doesnot compute quantitative geometry from the image. However, thequantitative geometry of the structure represented in one or more imagesmay contain valuable information about the structure that can be used todiagnose disease, assess the efficacy of treatment and/or perform otheranalyses of the structure. Such quantitative information about thestructure is beyond the capability of conventional human visual imageunderstanding alone.

Image processing techniques have been developed to automate or partiallyautomate the task of understanding and partitioning the structure in animage and are employed in computer aided diagnosis (CAD) to assist aphysician in identifying and locating structure of interest in a 2D or3D image. CAD techniques often involve segmenting the image into groupsof related pixels and identifying the various groups of pixels, forexample, as those comprising a tumor or a vessel or some other structureof interest. However, conventional segmentation may produceunsatisfactory or incomplete results, particularly when the structurebeing detected appears in the image at arbitrary locations, sizes andorientations. As a result, the limited geometry that may be extractedfrom conventional image processing may be unsuitable for use in furtheranalysis based on the extracted geometry.

SUMMARY OF THE INVENTION

Applicant has developed methods and apparatus for extracting geometryfrom images, scan data, and/or representations of tubular bodystructures (e.g., blood vessels or other body vessels). Aspects of theinvention relate to obtaining vessel geometry, determining one or morestructural features from the vessel geometry, and/or analyzing the oneor more structural features for medical diagnostic, prognostic, and/orresearch applications.

Applicant has developed methods and apparatus for extracting geometryfrom images, scan data, and/or representations of tubular bodystructures (e.g., blood vessels or other body vessels). Aspects of theinvention are useful for obtaining a geometrical representation of avascular tree that contains data relating to three-dimensional location,orientation and/or size at any point in the vascular tree of a subject.In some embodiments, a vascular tree may be represented by a series ofdisks or poker chips (e.g., circular or eliptical disks) that are linkedtogether to form a three-dimensional structure containing informationrelating to the local size, shape, branching, and other structuralfeatures at any point in the vascular tree.

It should be appreciated that the entire vascular tree of a subject maybe represented by a network of linked poker chips (e.g., circular oreliptical disks). However, in many embodiments, only a subset or aportion of a vascular tree may be represented or analyzed. In someembodiments, a portion of a vascular tree can be represented by a singledisc or poker chip that contains information relating to the location ofthe center of the vessel, vessel size (diameter), and/or orientation(e.g., the direction of the centerline of the vessel). In someembodiments, a portion of a vascular tree may be represented by adataset that describes one or more poker chips along with informationrelating to the linkage between the poker chips within a region ofinterest of the vascular tree.

Some embodiments includes a method of detecting at least one featureassociated with a blood vessel in at least one image of at least oneblood vessel using a matched filter adapted to respond to the at leastone feature, the method comprising applying a scale detection filter toselected voxels in the at least one image to determine a scale for thematched filter at each of the selected voxels, determining anorientation for the matched filter at each of the selected voxels,wherein determining the orientation is assisted by using the scaledetermined at each of the selected voxels, applying the matched filterat each of the selected voxels at the scale and the orientationdetermined at each of the selected voxels to obtain a filter response ateach of the selected voxels, and analyzing the filter response at eachof the selected voxels to determine if the respective voxel correspondsto the at least one feature.

According to some embodiments, the at least one feature includes theintensity at centerline voxels, which are detected using a matchedfilter, wherein the detected centerline voxels are further analyzed tolink the centerline voxels together to provide adjacency and vesselmembership information.

Some embodiments include applying an orientation independent scalefilter that is invariant to direction to detect scale at voxels in theimage. Some embodiments include an orientation independent scale filterthat is independent of orientation detection and/or feature detection.Some embodiments include a first derivative orientation detectionoperation performed separately from scale detection. Some embodimentsinclude a matched filter using a step function to detect vessels, thematched filter being applied using the scale and orientation determinedduring the separate scale detection and orientation detection.

Some embodiments include a method of determining a scale at each of aplurality of selected voxels in at least one image of at least one bloodvessel, the scale at each of the plurality of selected voxels beingdetermined using an orientation independent scale detection filterhaving a filter size defined by a radius, wherein the scale is used todetermine the size of a matched filter adapted to respond to at leastone feature associated with the at least one blood vessel, the methodcomprising (A) selecting a target voxel from the plurality of selectedvoxels at which to determine the scale, (B) setting the radius to apredetermined minimum value so that the filter size is at apredetermined minimum, (C) applying the orientation independent scaledetection filter at the target voxel to obtain a filter response, (D)comparing the filter response with a predetermined criteria, (E)increasing the value of the radius of the orientation independent scaledetection filter to increase the filter size of the orientationindependent scale detection filter if the filter response meets thepredetermined criteria, (F) performing acts (A)-(F) with increasedfilter size if the filter response meets the predetermined criteria, and(G) setting the scale based on the value of the radius of theorientation independent scale detection filter if the filter responsedoes not meet the predetermined criteria.

Some embodiments include a method of linking geometry obtained from atleast one image of at least one blood vessel, the geometry including aplurality of locations in the at least one image determined to beassociated with voxels representing the centerline of a vessel, each ofthe plurality of locations having an associated orientation indicativeof a direction of the centerline of the vessel and an associated filterresponse resulting from applying a centerline filter centered at therespective location, the method comprising linking centerline voxelsbased on one or more of the following parameters: a distance betweencenterline voxels; a change in the orientation of the centerline betweencenterline voxels; a change in the filter response between centerlinevoxels; and a change in vessel radius between centerline voxels. Thecenterline voxels may be linked to form a linked Poker Chiprepresentation.

Some embodiments include a method of linking geometry obtained from atleast one image of at least one blood vessel, the geometry including aplurality of locations in the at least one image determined to beassociated with voxels representing the centerline of a vessel, each ofthe plurality of locations having an associated orientation indicativeof a direction of a centerline of the vessel and an associated filterresponse resulting from applying a centerline filter centered at therespective location. The method comprises selecting a target locationfrom the plurality of locations, comparing the target location with eachother location in the plurality of locations within a predeterminedneighborhood, wherein comparing includes, determining a distance betweenthe target location and each of the other locations, determining adifference between the orientation at the target location and theorientation at each of the other plurality of locations, and determininga difference between the filter response at the target location and thefilter response at each of the other plurality of locations, and linkingthe voxel associated with the target location with the voxel associatedwith one of the other locations based, at least in part, on thecomparison.

According to aspects of the invention, a poker chip representation of avasculature may be mined for physiological, biological, and/or medicalpurposes. In some embodiments, geometrical information associated with asingle poker chip may be mined. In some embodiments, geometricalinformation associated with a plurality of poker chips, optionallyincluding local linkage information may be mined. Accordingly, aspectsof the invention relate to obtaining vessel geometry, determining one ormore structural features from the vessel geometry, and/or analyzing theone or more structural features for medical diagnostic, prognostic,and/or research applications.

Aspects of the invention provide methods for analyzing structures suchas blood vessels and evaluating their association with disease,responsiveness to therapeutic treatments, and/or other conditions.Aspects of the invention provide quantitative and analytical methods forevaluating and/or comparing the vessels in different regions of the samebody (e.g., a human body) or within ex vivo tissues or between differentbodies (e.g., the same regions in different bodies) or different ex vivotissues. Aspects of the invention can be useful in assisting and/orautomating the analysis of vascular patterns and their association withdisease diagnosis, prognosis, response to therapy, etc., or anycombination thereof. Aspects of the invention can be used in connectionwith vessel structural information that is obtained from vessel images(e.g., blood vessel images), scan data, vessel representations (e.g., areconstructed vasculature, a representation that can be viewed as beingsimilar in some ways to a stack of poker chips with varying diametersand is that is referred to herein as a Poker Chip representation, or anyother useful representation, or any combination thereof).

Methods are provided for analyzing vessel structural features, and bloodvessel structural features in particular. In some embodiments, adistribution of vessel parameters (e.g., structural features ormorphological parameters) within a region of interest may be generatedand evaluated. In some embodiments, the vessel parameters may relate tothe size, shape, or number of vessels with a region of interest. Adistribution may be generated based on quantitative measurements relatedto one or more parameters. In some embodiments, a distribution of bloodvessels may be a population distribution of blood vessels as a functionof quantitative measures of one or more parameters. For example, adistribution may represent the number of blood vessels (or thepercentage of the blood vessel population) as a function of theirdiameter, branching frequency, distance between branches, degree oftortuousity, curvature, or any other quantitative structural feature ormorphological parameter, e.g., as described herein, or any combinationof two or more thereof. In some embodiments, a distribution may bedivided into groups or bins representing different value ranges of thequantitative measurements (e.g., ranges of vessel diameters such as 0-30microns, 30-60 microns, 60-90 microns, 90-120 microns, 120-150 microns,150-180 microns, etc., or any combination thereof). It should beappreciated that a distribution may be represented in any suitable form,for example graphically (e.g., a graph or histogram), in the form of atable, as a database, in a computer-readable or computer storage medium,etc., or any combination thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a flow chart of extracting geometry from an image, inaccordance with some embodiments of the invention;

FIG. 2 illustrates a geometrical representation of vessel structure,referred to as the Poker Chip representation, in accordance with someembodiments of the present invention;

FIG. 3A illustrates a cylindrical segment used to model vesselstructure, in accordance with some embodiments of the present invention;

FIG. 3B illustrates a grey scale representation of a characteristicfunction of a model used to detect vessel structures, in accordance withsome embodiments of the present invention;

FIG. 3C illustrates a plot of the intensity values along the x-axis atthe center of the grey scale Gaussian distribution in FIG. 3B;

FIG. 3D illustrates a plot of the intensity values along the x-axis ofanother model of vessel intensity profile;

FIG. 4 illustrates schematically a cylindrical vessel segment intensitydistribution illustrating a ridge or centerline feature, in accordancewith some embodiments of the present invention;

FIG. 5 illustrates an embodiment of a mixture of truncated Gaussian fitto 3D reconstruction intensity data, wherein the vertical axis is in logscale and low part of the horizontal axis is shown;

FIG. 6 illustrates an embodiment of a theoretical profile of acenterline filter response using scale detection, in accordance withsome embodiments of the present invention;

FIG. 7 illustrates an embodiment of a detected scale versus the choiceof threshold a;

FIG. 9 illustrates an embodiment of how R(X, r) behaviors on realimages—(a) a slice of 3D images is shown and blue point is the point Xwhere we apply rank-based scale filter—(b) the rank-based scale filter'sresponse with different radius is shown—although the intensities havelarge variation inside vessel, the rank-based scale filter behaviorsmoothly and have a rapidly decay while cross the boundary of thevessel;

FIG. 10A illustrates a centerline filter, in accordance with someembodiments of the present invention;

FIG. 10B illustrates a profile of the centerline filter illustrated inFIG. 9A along the line x-x′, in accordance with some embodiments of thepresent invention;

FIG. 10C illustrates another profile of the centerline filterillustrated in FIG. 9A along the line x-x′, in accordance with someembodiments of the present invention;

FIG. 11 illustrates centerline filtering on a 3D volume data set, inaccordance with some embodiments of the present invention;

FIG. 12 illustrates net volume of the center line filter versusdifferent scales;

FIG. 13 illustrates a geometrical representation of vasculature obtainedfrom a 3D volumetric image, in accordance with some embodiments of thepresent invention;

FIG. 14 illustrates blood vessel size distribution in an example ofcasts of a xenograft tumor model after treatment with Avastin® (ananti-angiogenic agent available from Genentech, South San Francisco,Calif.), in accordance with some embodiments of the present invention;

FIG. 15 illustrates the vessel population ratio between small and middlesize vessels in an example of casts of a xenograft tumor model aftertreatment with Avastin®, in accordance with some embodiments of thepresent invention;

FIG. 16 illustrates the vessel population ratio between large and middlesize vessels in an example of casts of a xenograft tumor model aftertreatment with Avastin®, in accordance with some embodiments of thepresent invention.

FIG. 17 illustrates the vessel population distribution in an example ofcasts of a tumor model after treatment with Avastin®, in accordance withsome embodiments of the present invention;

FIG. 18 illustrates the vessel population ratio between small and middlesize vessels in an example of casts of a tumor model after treatmentwith Avastin®, in accordance with some embodiments of the presentinvention; and

FIG. 19 illustrates the vessel population ratio between large and middlesize vessels in an example of casts of a tumor model after treatmentwith Avastin®, in accordance with some embodiments of the presentinvention.

DETAILED DESCRIPTION

As discussed above, analyzing vessel structures (e.g., blood vesselstructures) and identifying structural profiles that are characteristicof one or more physiological conditions or responses (e.g., positiveresponses to pharmaceutical compounds) may be of interest in many areasof diagnostics, therapeutics and/or treatment. However, the amount ofinformation that can be directly obtained or ascertained from image data(e.g., x-ray, CT, MRI, etc.) may be prohibitively limited in thisrespect. Accordingly, Applicant has recognized the benefit of developingmethods of extracting geometry from images to facilitate the abovedescribed analysis.

To extract geometrical properties of vessel structures in one or moreimages, the vessels must first be detected in the image and representedin a meaningful fashion. Various methods have been proposed fordetecting one or more features of a blood vessel using a filter adaptedto respond to the one or more features. For example, filters have beendesigned to respond to the intensity profile of a vessel to locatevoxels that exhibit this intensity profile. However, conventionalfiltering techniques may be unsatisfactory at accurately and robustlydetecting vessel structures in one or more images. Filtering techniquestypically require some additional preprocessing to obtain informationabout the image to improve the filtering process. For example, the scaleof the structure at a particular location in the image may be obtainedto determine what size filter should be used at that location. That is,not only should the filter match the feature being detected, in order torespond correctly, the filter should also match the scale of thefeature. Moreover, because the orientation of the feature being detectedis not known a priori, filtering techniques often include somepreprocessing to determine the orientation of the feature at aparticular location so that the filter can be applied to the image ingeneral alignment with the feature.

Conventionally, scale detection and orientation detection are performedsimultaneously. Applicant has appreciated that simultaneous scale andorientation detection may result in sub-optimal detection of eitherscale, orientation or both. As a result, subsequent filtering to detectone or more features applied using sub-optimal scale and orientationparameters may be substantially degraded. Applicant has developed amethod for detecting vessel features that includes a scale detectionoperation and an orientation detection operation that are performedseparately. In some embodiments, scale detection is performed prior toorientation detection, and orientation detection is performed using thescale determined by the scale detection. The scale and orientationvalues determined from the separate scale and orientation detectionoperations may then be used to apply the feature detection filter, forexample, a centerline filter adapted to respond to the centerline voxelsof blood vessels.

According to some embodiments, scale detection employs an orientationindependent scale detector such that scale detection may be performedindependent of orientation detection. According to some embodiments, anorientation independent scale filter is used having a filter kernel thatis symmetric with respect to orientation such that the filter does notrely on orientation for accurate scale detection. According to someembodiments, the orientation independent scale filter includes a filtersize defined by a radius. At each of a plurality of selected voxels inan image, the orientation independent scale filter is applied atincreasing radii until the filter response fails to meet a predeterminedcriteria. The largest radius at which the filter response meets thepredetermined criteria is used to represent the scale. According to someembodiments, the diameter of vessel structures in the images isdetermined based on this largest radius. That is, according to someembodiments, at least some geometry of vessel structures may bedetermined by the scale detection operation.

Applicant has appreciated that performing scale detection, orientationdetection and centerline detection provides, at each detected centerlinevoxel, the location, the direction of the centerline and the radius ofthe vessel. This geometry can be used to analyze vascular structure andthese geometrical parameters have been used to develop a mathematicalrepresentation of the detected vessel structure. In some embodiments,each centerline location may be represented as a circular or elipticaldisk having a center at the centerline location, a radius correspondingto the associated scale, and a normal vector to the disk (e.g., circulardisk) corresponding to the direction of the centerline as determinedduring orientation detection. This representation resembles a poker chipand is referred to herein as the Poker Chip representation, as describedin further detail below.

While the Poker Chip representation provides much useful informationabout the geometry of the vessel, without further processing, there isno notion of adjacency or vessel membership, which may be usefulinformation in performing analysis on the vasculature. Accordingly, insome embodiments, each of the detected centerline voxels (e.g., centerlocations of a poker chip) are linked together to capture adjacencyinformation as well as vessel membership. In some embodiments, thecenterline voxels are linked according to a criteria that includes oneor any combination of minimizing a distance, a direction change, aradius change and/or a filter response change from a centerline voxel toan adjacent centerline voxel. That is, when selecting between a numberof candidate centerline voxels to link to a target centerline voxel, thecenterline voxel candidate that creates the smallest change in one ormore of the above parameters may be preferred over candidate centerlinevoxels having larger changes. The linked centerline voxels can then beused to compute various structural characteristics of the vasculatureformed by the detected vessels as represented by the stacked and linkedpoker chips.

Following below are more detailed descriptions of various conceptsrelated to, and embodiments of, methods and apparatus according to thepresent invention. It should be appreciated that various aspects of theinvention described herein may be implemented in any of numerous ways.Examples of specific implementations are provided herein forillustrative purposes only. In addition, the various aspects of theinvention described in the embodiments below may be used alone or in anycombination, and are not limited to the combinations explicitlydescribed herein.

FIG. 1 illustrates a method of extracting vessel geometry from one ormore images of vasculature, in accordance with some embodiments of thepresent invention. Act 110 includes obtaining image information of atleast a portion of a vasculature structure. For example, the imageinformation may be a two-dimensional (2D), three-dimensional (3D) orother dimensional image obtained from scanning an object using x-ray CT,MRI, PET, SPECT, etc. The scanned object may be a live specimen such asa human or other animal (i.e., an in-vivo scan), or obtained from a castof a specimen's vasculature.

The method of FIG. 1 may be performed on any image of any dimensionindependent of how the image was obtained, as the aspects of theinvention are not limited in this respect. In 2D images, each 2Dlocation having an associated intensity is conventionally referred to asa pixel. In 3D images, each volume location having an associatedintensity is conventionally referred to as a voxel. The term voxel isused herein to refer to both 2D and 3D image locations to eliminate theneed to specify the dimensionality of the images, as the methodsdescribed herein are generic to dimensionality.

Many techniques for extracting information from images use variousfiltering techniques. For example, filters are often designed such thatwhen applied to a portion of an image (e.g., convolved with a portion ofthe image) the filter response is relatively large when the filter isapplied to an image portion having a feature or characteristicindicative of structure being detected in the image, and relativelysmall otherwise. The filter detection described below in connection withact 140 is one example of matched filtering. However, other filteringtechniques may be used, as the aspects of the invention are not limitedin this respect.

When the feature or structure being detected appears in an image atdifferent sizes or scales, the size of the filter kernel should beadjusted to the appropriate scale in order for the filter response toaccurately indicate the presence of the desired feature. For example, inan image containing biological vasculature, and in particular, tumorvasculature, the constituent vessels will typically vary greatly indiameter. Accordingly, a filter designed to detect relatively largevessels will not respond accordingly to small vessels, even when appliedon the correct location. However, it is not known a priori where largeand small vessels are located. Accordingly, successful detection mayrequire determining the scale of the structure in the image prior toapplying the filter. This technique is herein referred to as “scaledetection.” Scale detection may be performed on predetermined portionsof an image, or may be determined on a voxel by voxel basis, asdescribed in further detail below.

In addition to detecting the appropriate scale, it may be beneficial todetect the orientation in which the filter should be applied. Inparticular, the feature(s) being detected may appear in the image atarbitrary orientations. For example, in the case of vasculature, thevessel properties being detected may be oriented in any arbitrarydirection. Accordingly, even if a filter at the appropriate scale isapplied at an image region corresponding to the feature being detected,the filter response may be relatively low if it is not oriented ingeneral alignment with the direction of the feature for which the filterwas designed to detect. Accordingly, determining the orientation of thefeatures or properties being detected may benefit filter detectiontechniques. This technique is herein referred to as “orientationdetection.”

Conventional filtering techniques combine scale and orientationdetection in a single operation. That is, the combination of possiblescales and orientations are tested simultaneously and the scale andorientation are selected when the response is maximum. However,Applicant has appreciated that maximum responses may not correspond tooptimal scale and optimal orientation simultaneously. Because theresponse is a combination of scale and orientation, one or both may besub-optimal while together providing a strong response. Applicant hasdeveloped a scale detection operation that is orientation independent.As a result, the operations of scale detection and orientation detectionmay be separated into two separate operations. In addition, the detectedscale may then be used to improve subsequent orientation detectionprocesses.

In act 120, scale detection is performed independently of orientationdetection. In some embodiments, scale detection 120 is performed using afilter that is independent of orientation. Scale detection 120 mayprovide the scale in the image at different regions in the image. Insome embodiments, scale detection 120 determines scale at each voxel inthe image. Alternatively, a preprocessing operation may be performed toroughly determine which voxels in the image correspond to subject matterof interest (e.g., vessels) and which voxels correspond to background.Scale detection may then be performed only on pixels determined tocorrespond to subject matter of interest, thus reducing the amount ofcomputations. The result of scale detection is a scale associated witheach location at which the filter was applied (e.g., a scale at eachselected voxel in the image). An orientation independent scale detectionalgorithm according to some embodiments is described in further detailbelow.

In act 130, orientation detection may be performed. To assist in moreaccurate orientation detection, the scale at the selected regions of theimage determined during scale detection 120 may be provided to theorientation detection operation. As discussed above, determining theorientation of subject matter of interest in one or more images may beimportant for accurate filter detection of the subject matter ofinterest (e.g., structure, feature, property or characteristic). Forexample, in embodiments where the subject matter of interest isvasculature, it may be important to detect the direction of the centeror longitudinal axis of the vessels before applying a filter thatdetects the centerline of the vessel. In some embodiments, the scaledetermined from scale detection 120 may be used to improve orientationdetection accuracy. The result of orientation detection is anorientation or direction at each selected voxel indicating the directionof the centerline at the respective location. An orientation detectionalgorithm according to some embodiments is described in further detailbelow.

In act 140, filter detection may be performed. In filter detection 140,a filter designed to respond to the subject matter of interest in theimage may be applied. In some embodiments, the filter is applied at thescale and/or orientation determined from scale detection and/ororientation detection, respectively. The magnitude of the filterresponse at selected locations in the image indicates the likelihoodthat the location includes the subject matter of interest. In someembodiments, the subject matter of interest is vasculature and thefilter is designed to respond to the center of a vessel. That is, thefilter may be designed to respond to the intensity profile across avessel and thus respond most strongly when centered on a centerlinevoxel in the direction of the intensity profile. Because the scale anddirection of the subject matter of interest has been determined atselected locations in the image, filter detection may appropriatelyaccurate in detecting the subject matter of interest. Several methods ofcenterline filtering are discussed in detail below, in accordance withsome embodiments of the present invention.

In act 150, non-maximal suppression may be performed on the output ofthe filter detection operation performed in act 140. As discussed above,the result of a filtering operation (e.g., centerline filtering)generally includes the filter response at each voxel at which the filterwas applied. The magnitude of the response is typically proportional tothe likelihood that the feature being detected is present at thecorresponding voxel location. However, it should be appreciated thatmany voxel locations will have associated non-zero filter responses. Inaddition, some voxel locations will have associated local maximum filterresponses even though the true location of the feature is elsewhere.However, accurate detection may require discriminating between localmaximum and the true maximum location, which corresponds to the mostlikely location of the structure being detected. Non-maximal suppression150 attempts to eliminate or suppress all but the true maximum filterresponses to accurately detect the subject matter of interest. Adetailed description of non-maximum suppression in the context ofcenterline filtering for vessel detection is described below.

In act 160, linking may be performed. Linking may include variousoperations that associate voxel locations with each other to formrelated structures so that geometric properties may be obtained from thelinked voxels. For example, in the context of vessel detection, thevoxel locations that were determined as centerline voxels aftercenterline detection and non-maximum suppression may be linked togetherto form the associated centerline of vessels. That is, analysis may beperformed to link together centerline voxels that are likely to havearisen from the same vessel structure. In such a way, the geometry ofthe vessels may be obtained (e.g., geometry 15). Methods for linkingvoxels in the context of vessel detection are described in furtherdetail below.

As discussed above, some embodiments are directed to detectingvasculature and extracting the geometry of the vasculature to facilitatevarious analysis such as diagnosis, therapeutics, drug efficacy, etc.Applicant has developed methods for extracting geometrical informationfrom 3D volumetric images using a match filter based system to segment avessel network and extract a mathematical (geometry) vesselrepresentation. Some embodiments of a vessel representation are referredto herein as the Poker Chip representation due to the similarity to astack of poker chips. The Poker Chip representation treats a vessel asan aggregation of infinitesimal cylinder cross-sections withcontinuously varying diameters. While in theory the “thickness” of eachpoker chip is infinitesimal, in practice the thickness of each pokerchip may be related to the resolution of the image(s) from which thegeometry was extracted. Thus, each poker chip may have associatedgeometry including, for example, center location, radius andorientation, as discussed in further detail below.

FIG. 2 illustrates a schematic of the Poker Chip representation.According to some embodiments, each poker chip 210 is defined by acenter location, a radius and an orientation. The center location c_(i)represents the center of the vessel, for example, determined bycenterline filtering, as discussed in further detail below. The radius rrepresents the radius of the vessel at location c_(i) and theorientation is the angle of the normal of the poker chip at locationc_(i), and represents the tangent of the centerline of the vessel atlocation c_(i). It should be appreciated that the Poker Chiprepresentation may include additional parameters, as the aspects of theinvention are not limited in this respect.

Applicant has appreciated that the above Poker Chip representation maybe used to determine characteristics of the vasculature that may help indiagnosing disease, providing information on appropriate treatment,and/or assessing the effectiveness of treatment. For example, since theorientation is known at each location, higher level information such ascurvature and tortuosity may be computed, as well as vessel density anddistribution measures, as discussed in further detail below.Additionally, since vessel diameter may be determined, vessel size andthe change in vessel sizes may be computed as well. Various analysesthat can be performed using the Poker Chip representation are discussedin further detail below.

To compute some of the higher order information, it may be beneficial toalso include in the Poker Chip representation information aboutneighboring poker chips. For example, information about how the pokerchips link together may be valuable in understanding the vesselstructure as a whole. As discussed above, Applicant has developedalgorithms that facilitate linking poker chips together to providemembership information with respect to which poker chips belong to whichvessel and information regarding which poker chips are adjacent to oneanother. After linking has been achieved, more sophisticated vesselanalysis may be performed.

Following below is a more detailed description of algorithms capable ofextracting geometry from 3D images to obtain a Poker Chip representationof vasculature present in the images, in accordance with someembodiments of the present invention. While the various algorithms arediscussed in connection with detecting and extracting vesselinformation, the concepts disclosed herein may be applied to detect andassociate other structure, as the aspects of the invention are notlimited in this respect. In addition, it should be appreciated thatdistribution analyses according to various aspects of the invention maybe applied to information obtained from any vessel image,representation, or combination thereof.

FIG. 3A illustrates one example of a cylindrical segment 300 that may beused to generally model a vessel segment. A configuration of cylindricalsegment 300 may be described by a number of parameters in a particularcoordinate frame. The position of cylindrical segment 300 may bedescribed by a location of the cylindrical axis 305 at a point (x_(i),y_(i), z_(i)) in space, for example, the origin or termination of thecylindrical segment. The orientation of cylindrical segment 300 may bespecified by the angle θ_(i) from the x-axis and the angle y_(i) fromthe y-axis. Since cylindrical segment 300 is axially symmetric, itsrotation about the z-axis may not need to be specified. The length ofthe cylindrical segment may be specified by l_(i) and the radius of thecylindrical segment 300 may be specified by r_(i).

Applicant has appreciated that the cross-section of a vessel may becharacterized by a generally Gaussian shaped intensity distribution. Thecross-sectional density of a vessel may be modeled by a Gaussiandistribution, centered on the longitudinal axis of the vessel, so thatthe modeled density is the highest at the center of the vessel. Forexample, the cross-sectional density distribution of a cylindricalvessel segment, when oriented such that its longitudinal axis coincideswith the z-axis, may be modeled as,

$\begin{matrix}{\rho\left( {\mathbb{e}}^{{- \frac{1}{r^{2}}}{({{({x - x_{i}})}^{2} + {({y - y_{i}})}^{2}})}} \right)} & (1)\end{matrix}$

where ρ is the density coefficient at a center of the cylindricalsegment and r is the radius of the cylindrical segment, so that thedensity is modeled as being greatest at the center (i.e., equal to ρ)and decays exponentially as a function of radial distance from thecenter. FIG. 3B illustrates a grey scale representation of the functiongiven in Eq. (1), where darker grey scale values indicate increaseddensity values. FIG. 3C illustrates a plot of the intensity values alongthe x-axis at the center of the grey scale Gaussian distribution in FIG.3B. FIG. 3D illustrates a vessel intensity profile that may better modelthe intensity profile of vessels in an image. Curve 1 and 2 illustratedvessel profile intensity when vessel diameter is larger than theresolution of the scan and when the vessel diameter is smaller,respectively.

The density distribution along the longitudinal axis of the cylinder(i.e., into and out of the page in FIG. 3B) is substantially uniform anddoes not vary substantially and may be modeled as a constant function ofthe cross-sectional distribution along the longitudinal axis, that is,as a constant function of the radial distance d from the center of thedistribution. FIG. 4 illustrates schematically a cylindrical vesselsegment intensity distribution model. In particular, the model of thecylindrical vessel segment has a maximum density at the center thatdecays exponentially to the boundary of the vessel as a function of theradial distance d, from the center. At each distance d, the density isuniform along the z-axis. For example, the density at d=0 is the densitymaximum along the length of the vessel. This density maximum shown byline 405 is referred to as a ridge, and corresponds to the centerline ofa vessel.

If the herein described characteristic intensity distribution or similardistribution can be identified in the image, the associatedpixels/voxels are likely to belong to a vessel. The characteristicpoints may be used to facilitate segmenting the image into vessel andnon-vessel regions. Some methods of detecting the characteristic shapeillustrated in FIG. 4 include performing ridge detection on an image. Aridge point is defined herein as a point in an image wherein theintensity assumes a local extrema in the direction of principalcurvature, i.e., the direction having the steepest intensity gradient.For example, at point 415 (and along ridge 405) in FIG. 4, the principaldirection of curvature is shown by u₀ (i.e., the unit vector (1,0) inthe (d, z) coordinate frame). Each point along ridge 405 forms a ridgepoint since each point is a local maximum along the z-axis. Accordingly,a ridge may be characterized by local derivative information in theimage and may be detected by examining the curvature of intensity aboutpoints of interest in the image.

Some conventional methods have proposed detecting the ridge using theHessian operator. However, the Hessian operator requires performingsecond derivatives of the image information, which reduces thesignal-to-noise ratio (SNR) and may result in degraded performance.Applicant has developed methods of detecting the characteristic shape ofblood vessels described above using centerline filtering techniques thatmay avoid some of the performance degradations commonly seen withconventional filters such as the Hessian operator, as discussed infurther detail below.

As discussed above in connection with FIG. 1, a non-limiting example ofa method for extracting geometry from images may include a number ofprocessing blocks including: a scale detector, an orientation detector,centerline filtering, non-maximum suppression and linkage. Brieflyspeaking, the system works as follows: firstly, the scale detection andorientation detection modules may be applied on 3D images to obtaincorrect size and orientation parameters for centerline detection (e.g.,scale and orientation parameters for the centerline filters); secondly,based on the parameters obtained from scale detection and orientationdetection modules, the centerline filter may be applied on every voxelof a 3D image, or applied on a subsection of voxels for which centerlinedetection is desired. The generated response field formed by applyingthe centerline filter indicates the likelihood that the associated voxelcorresponds to the vessel centerline; finally, non-maximum suppressionand linkage is applied on the centerline response field to extract thevessel centerline and obtain a vessel mathematical representation (e.g.,a linked Poker Chip representation). Following below are more detaileddescriptions of embodiments of the five main blocks briefly discussedabove, e.g., scale detection, orientation detection, centerlinefiltering, non-maximum suppression and centerline linking.

Scale Detection

As discussed above, scale detection may be applied to estimate thecenterline filter size appropriate for each voxel at which centerlinedetection is to be applied. Applying scale detection on each voxel of a3D image volume may be relatively expensive computationally. That is, ifeach voxel in the 3D image is deemed to be a potential centerline point,then scale detection should be applied to each voxel in the image.However, Applicant has appreciated that since vessels occupy only aportion of the volume, it may not be necessary to detect scale on everyvoxel. In particular, certain voxels may be eliminated based on theimage properties of the voxels, for example, the intensity level of thevoxel.

In general, intensities from vessels are higher than those in thebackground. Using a conservative intensity threshold, voxels may beclassified as background voxels with a low false positive rate that canbe controlled based on how conservative the threshold operator is set.That is, by setting the threshold conservatively, a substantialpercentage of the background voxels may be eliminated from scaledetection without the risk of eliminating any vessel voxels. The term“background” refers herein to voxels that are not part of the subjectmatter of interest that is being detected. By eliminating backgroundvoxels, the computations needed to perform scale detection can bereduced. That is, by removing at least some voxels from consideration,scale detection need not be performed on each voxel in the image.

It is reasonable to model both background intensity and vesselintensities as a Gaussian distribution. In practice, the assumption inFIG. 5 shows that a model using a mixture of truncated Gaussians is avery good fit for the data in low intensity regions. The truncatedGaussian distribution has the Probability Density Function (PDF) asfollows:

$\begin{matrix}{{p\left( {{I/\mu},\sigma} \right)} = \frac{N\left( {{I❘\mu},\sigma} \right)}{\int_{b_{1}}^{b_{2}}{{N\left( {{x❘\mu},\sigma} \right)}{\mathbb{d}x}}}} & (2)\end{matrix}$

where N(I|μ, σ) denotes a Gaussian distribution with mean μ and varianceσ, and b1 and b2 are the truncation points. To capture both backgroundand vessel distributions, the mixture of two truncated Gaussians for thedata may be expressed as:

$\begin{matrix}{{p(I)} = {\sum\limits_{c = 0}^{1}{\sum\limits_{i}\left\{ {w_{c}{\log\left\lbrack \frac{N_{c{({{I_{i}❘\mu_{c}},\sigma_{c}})}}}{\int_{b_{1}}^{b_{2}}N_{{c{({{x_{i}❘\mu_{c}},\sigma_{c}})}}{\mathbb{d}x}}} \right\rbrack}} \right\}}}} & (3)\end{matrix}$

where w_(c) is the weight percentage of each component. Directlymaximizing the likelihood may become challenging because determining themarginal probability may require computations that increaseexponentially with the data. In some embodiments, the problem is solvedusing an Expectation Maximization (EM) algorithm. The EM processiteratively goes through two steps by soft assignment of data(Expectation) and maximizing the whole likelihood (Maximization). Thatis, an initial approximate distribution may be used to classify voxelsas either background or foreground (e.g., vessels) in the Expectationstep. Next, the distribution is refined based on the classification(Maximization) and classification (Expectation) is repeated on therefined distribution. This process may be repeated until the processconverges on a final classification of background and foreground voxels.

Applying an EM algorithm on a mixture of Gaussians is only one method bywhich background voxels may be eliminated from consideration, or bywhich voxels are classified as background and foreground voxels. Otherpreprocessing or thresholding techniques may be used to reduce thenumber of voxels on which further processing is performed to reduce thecomputational expense, as the aspects of the invention are not limitedin this respect. In addition, while voxel intensity may be one suitableparameter to use to perform a conservative elimination of voxelsbelonging to the background, any suitable parameter may be used, as theaspects of the invention are not limited in this respect. For example,higher order properties may be used.

As discussed above, separating scale detection and orientation detectionmay have benefits over algorithms that perform the two operationssimultaneously. Applicant has designed a scale detection filter whichdoes not depend on the orientation of the structure to be detected.According to some embodiments, an orientation independent filter may bedeveloped such that the filter can be mathematically described inspherical coordinates as f=f(r), which is a function that does notdepend on orientation. The symmetry of the filter allows the filter tobe independent of how the filter is oriented. To accurately detectcenterline voxels from 3D images, the response generated by the scaledetection filter should be maximum when it is located at a centerlinevoxel. The scale σ_(r) at a point (x, y, z) inside a cylinder may bedefined as the distance to the wall of the cylinder boundary:σ_(r)(x,y,z)=dist(x,y,z; wall of the cyclinder)  (4)

As shown in FIG. 6, this definition of scale guarantees a unique maximumfilter response inside the cylinder after scale selection (in theabsence of noise). Normally, the intensity of a 3D image outside of avessel is significantly lower than the intensity inside the vessel. Thisrapid intensity decay provides an indication of scale. Applicant hasdeveloped a rank-based scale filter that is orientation independent.Given a point X inside a vessel, a rank based scale filter may bedefined as:

$\begin{matrix}{{\mathcal{R}\left( {X,r} \right)} = \frac{f_{-}\left( \left\{ {{{I\left( X^{\prime} \right)} :: {{X^{\prime} - X}}} = {r + 1}} \right\} \right)}{\min_{r}\left\{ {f_{+}\left( \left\{ {{{{I\left( X^{\prime} \right)} :: {{X^{\prime} - X}}} = 1},\ldots\mspace{14mu},r} \right\} \right)} \right\}}} & (5)\end{matrix}$

where R(X, r) is the filter response at image location X with filterradius r, and f⁻ and f₊ are rank functions, respectively. Note that thefilter is parameterized by radius only, resulting in filter symmetrythat is orientation independent. Given various noise models, there aremany ways to choose the rank functions. In order to cope with imagereconstruction effects, f⁻ may be chosen as the median value of the last10 lowest intensities and f+ may be chosen as the median value of thelast 10 highest intensities. That is, the rank function may bedetermined from characteristics of the image. However, the rankfunctions may be selected to be any value that facilitates detection ofscale, as the aspects of the invention are not limited in this respect.The scale σ_(r)(X) may then be obtained by finding the minimum radius rso that R(X, r) reaches the threshold α:

$\begin{matrix}{{\sigma_{r}(X)} = {\min\limits_{r}\left\{ {{R\left( {X,r} \right)} < \frac{1}{\alpha}} \right\}}} & (6)\end{matrix}$

Stated differently, the radius of the scale filter is increased untilthe filter response no longer satisfies the relationship in Eq. (6). Asdiscussed above, the scale detection filter may be designed to beindependent of orientation. According to some embodiments, the kernel orshell of the scale filter is a circle in 2D and a sphere in 3D. As aresult, the size of the filter is defined by the radius r, where thecenter of the filter is located at a target voxel at location X in theimage. Since the filter has the same radius in all directions, theapplication of the scale filter is independent of orientation.

The criteria for the filter response may be chosen to be any suitablecriteria that can robustly determine when the filter kernel has crosseda vessel boundary. The criteria in Eq. (6) is merely exemplary. In someembodiments, the value of α is chosen to be 5. However, other values maybe used as well as the aspects of the invention are not limited in thisrespect. In order to examine the sensitivities of this rank-based scalefilter to the choice of the threshold parameter α, a few points insidedifferent vessels may be randomly chosen to see how the selected scalechanges depending on the ratio threshold parameter α. FIG. 7 shows thatthe scale approaches the correct value when α is chosen to be largerthan 5.

FIG. 8 illustrates pictorial an orientation independent scale filter, inaccordance with some embodiments of the present invention. It should beappreciated that while the scale detection filter in FIG. 8 is shown(and is suitable) in the context of a 2D image for convenience ofillustration, the scale detection filter is designed as a 3D filter todetect scale in 3D volumetric images. In particular, the circular filterillustrated in FIG. 8 may be made an expanded to a sphere to detectscale in 3D. In FIG. 8, a portion of an image 805 is shown having avessel structure 815 within the image portion. It should be appreciatedthat image portion 805 is schematic and the vessel structure 815 and thebackground 825 would be comprised of an intensity value at each voxellocation in the image portion. Moreover, it should be appreciated thatimage portion 805 may be a small portion of a much larger image. For thesake of clarity only a single vessel structure is depicted in imageportion 805, though the image portion may in reality include any numberof vessel structures.

FIG. 8 also illustrates three separate applications of an orientationindependent scale filter 850. It should be appreciated that the scalefilter 850 may be applied at all of the image voxels or at a selectednumber of image voxels (e.g., voxels determined to be vessel voxelsusing a preprocessing techniques such as the intelligent thresholdingmethod described above). The three applications of the filter in FIG. 8are merely exemplary and are chosen at arbitrary locations to assist indescribing the scale detection filter. Each application of the filterbegins by placing the filter with a predetermined minimum radius r on atarget pixel at which scale is being detected. The scale filter is thenapplied to the image, for example, by convolving the image pixels thatfall under the filter kernel or support with the values of the filterkernel. If a certain criteria is met, the filter is assumed to still beentirely within the vessel and the radius r is increased.

In FIG. 8, the increasing of the filter radius is depicted by thesuccessively larger circles in dashed line. The circles in solid linedenote the last filter applied such that the criteria was met. Forexample, the dotted line circle in filter application 850 b shows acircle of r_(n) that when applied to the underlying image failed to meetthe criteria, where n is the number of successively larger radius filterkernels that have been applied to the image. Thus, the scale at thecorresponding image location is determined to be r_(n−1). Not only doesscale detection provide the appropriate scale to be used in subsequentfiltering processes (e.g., centerline detection), it also may indicatethe radius of the vessel structure in the Poker Chip representation.

Applicant has used the fact that the intensity of voxels within thevessel, in the absence of noise, is substantially higher than thebackground voxels to establish the criteria such that the criteria willnot generally be met when the filter kernel is extended outside thevessel structure. One embodiment of such a criteria is described in Eq.5 and Eq. 6. By employing the rank functions illustrated in Eq. 5, andusing the criteria in Eq. 6, a robust filter may be designed that willfail to meet the criteria when the filter kernel is increased in sizesuch that it encompasses voxels outside of the vessel. However, theabove described scale detection filter is exemplary and other scaledetection filters may be used, as the aspects of the invention are notlimited in this respect. In addition, any criteria that tends not to bemet as a filter is expanded across a vessel boundary may be used, as theaspects of the invention are not limited in this respect.

Because the centerline voxels are not known a priori, the scaledetection filter may be applied to non-centerline voxels. As shown byfilter application 850 b, the scale detection is again stopped when thefilter kernel crosses the vessel boundary. Because the target voxel isnot a centerline voxel, the radius of the filter will not correspond tothe radius of the vessel. However, this may be inconsequential becausevoxels that are not determined to be centerline voxels are removed insubsequent processing, such as during centerline filtering discussedbelow. Because only voxels detected as centerline voxels will survivecenterline filtering, the radius of the scale detector may accuratelyreflect the radius of the associated vessel.

FIG. 9 shows what R(X, r) looks like when it is applied on real images.Although the intensities have large variation inside the vessel, therank-based scale filter behaves smoothly and decays relatively rapidlyacross the boundary of the vessel. Thus, rank-based scale filters mayhave the generally beneficial property of relatively distinct responsechange as the filter crosses vessel boundaries, and is relatively stableand insensitive to the choice of ratio parameter. Accordingly, scale maybe detected at each selected voxel in the image. For example, scale maybe detected at each voxel in the image or the reduced number of voxelsresulting from performing thresholding on the image to eliminate atleast some of the background voxels. The selected voxels at which scaledetection is performed can be selected in other ways, as the aspects ofthe invention are not limited in this respect.

Orientation Detection

As discussed above, centerline filtering may be improved by firstdetermining the orientation at which the centerline filter should beapplied. Since scale is detected independent of orientation, orientationdetection may be performed separately from scale detection and, in someembodiments, orientation detection uses the scale values detected duringscale detection to improve detection of the orientation of the subjectmatter of interest. In some embodiments, a gradient based orientationdetection algorithm may be used, however, other algorithms may be usedto detect vessel orientation, as the aspects of the invention are notlimited in this respect. Because of the rotational symmetry along theaxis of a cylinder on which the vessel structure may be modeled, theintensity along a line parallel to the vessel axis is constant in theabsence of noise. In other words, the directional derivative ofintensity along the direction v parallel to the vessel axis is zero inthe absence of noise:v·∇ρ(X)=0  (7)

It should be appreciated that x-ray decay during image acquisitiondepends on its penetrating length. Thus, the intensity inside a vesseltends to vary along any direction other than the axis direction. Thisfact indicates that Eq. (7) may be a necessary and sufficient conditionfor finding the vessel direction since the above argument holds for anypoint X inside the vessel. Therefore, the direction of a small cylindersegment at each point X can be estimated by finding a direction vector aalong which the intensities have the least change. However, directestimation from the derivative of one point X tends to be error prone.In some embodiments, all the derivatives inside a small volume centeringon the point X may be used to increase the accuracy. To be more precise,the axis direction â may be estimated by finding a direction a thatminimizes the sum of the directional intensity gradient along thisdirection:

$\begin{matrix}{\hat{a} = {\arg{\min\limits_{a}\left\{ {\int{\int_{v}{\int{{{a \cdot {\nabla{\rho\left( {x,y,z} \right)}}}}{\mathbb{d}x}{\mathbb{d}y}{\mathbb{d}z}}}}} \right\}}}} & (8)\end{matrix}$

where σ(X) is the scale detected at point X and ∥·∥ is the normdiscussed herein. In the presence of noise, a directional gradient ofintensity convolved with an adaptive Gaussian kernel may be used, asfollows.

$\begin{matrix}{\hat{a} = {\arg{\min\limits_{a}\left\{ {\int{\int_{v}{\int{{{a \cdot {\nabla\left( {G_{\sigma({x,y,z}} \cdot {\rho\left( {x,y,z} \right)}} \right)}}}{\mathbb{d}x}{\mathbb{d}y}{\mathbb{d}z}}}}} \right\}}}} & (9)\end{matrix}$

In some embodiments, Eq. (9) can be solved by a least square estimationby assuming the noise distribution is Gaussian i.i.d, i.e., the norm inEq. (9) is an L2-norm. However, it is well known that an L2-norm may besensitive to outliers present in the input data, and outliers mayfrequently appear in reconstructed 3D images. In some embodiments, aL1-norm in Eq. (9) may be used.

$\begin{matrix}{\hat{a} = {\arg{\min\limits_{a}\left\{ {\int{\int_{v}{\int{{{a \cdot {\nabla\left( {G_{\sigma{({x,y,z})}} \cdot {\rho\left( {x,y,z} \right)}} \right)}}}_{1}{\mathbb{d}x}{\mathbb{d}y}{\mathbb{d}z}}}}} \right\}}}} & (10) \\{\arg{\min\limits_{a}\left\{ {\int{\int_{v}{\int{{{a}_{1} \cdot {{\nabla\left( {G_{\sigma{({x,y,z})}} \cdot {\rho\left( {x,y,z} \right)}} \right)}}_{1}}{\mathbb{d}x}{\mathbb{d}y}{\mathbb{d}z}}}}} \right\}}} & (11)\end{matrix}$

To avoid the trivial solution at a=0 in the above equation, theconstraint Σ₁∥a₁∥₂=1 may be used. Since a is independent of the point(x, y, z), a is moved out of the triple integral so that:

$\begin{matrix}{{\hat{a} = {\min\limits_{a}\left\{ {{a \cdot \underset{\underset{M}{︸}}{\int{\int_{v}{\int{{\nabla\left( {G_{\sigma{({x,y,z})}} \cdot {\rho\left( {x,y,z} \right)}} \right)}{\mathbb{d}x}{\mathbb{d}y}{\mathbb{d}z}}}}}}}_{L\; 2} \right\}}}{s.t.\mspace{14mu}\left\{ {{\sum\limits_{i}{a_{i}}_{2}} = 1} \right\}}} & (12)\end{matrix}$

It should be appreciated that in Eqs. (8)-(12), the operation is beingperformed over a volume v. By performing orientation detection over aneighborhood, rather than at a single voxel, semi-global information maybe captured in the orientation assessment. The neighborhood informationallows for robust orientation detection in the presence of noise andoutliers. However, it should be appreciated that the neighborhood (e.g.,the volume v) may be different for detecting direction in relativelylarge vessels versus relatively small vessels. Accordingly, Applicanthas developed an adaptive method that varies the size of theneighborhood based on the scale at a target voxel. That is, the scaledetermined during scale detection may be used to determine the size ofthe volume v. In some embodiments, the size of (2└s+2┘+1) may be used asthe size of volume. However, any adaptive neighborhood based on scalemay be used, as the aspects of the invention are not limited in thisrespect. Thus, the size of the neighborhood used for orientationdetection may be adapted according to the scale of the image at eachlocation.

As discussed above, and L1-norm may be used to address outliers. Thereare a number of ways to solve Eq. (12). In some embodiments, theequation is solved by constraint optimization using Lagrangemultipliers. Applying Lagrange multipliers to the above equationobtains:∇_(a)(a ^(T) M ^(T) Ma+λa ^(T) a)=0(M ^(T) M)a+λa ^(T)=0  (13)

Therefore the center line direction, a, may be obtained by computing theeigenvector associated with the smallest eigenvalues of matrix M.Referring back to FIG. 4, solving the above equations to determine thedirection a can be pictorial explained. In general terms, theeigenvectors of matrix M indicate the characteristic directions ofcurvature. The relationship between these characteristic directions ofcurvature may be employed to identify the direction of the centerline.The eigenvalues and associated eigenvectors of a matrix may bedetermined in various ways, for example, by any number of well knowniterative methods of diagonalizing a matrix or analytically by directlysolving the relationship:Mu=λu  (14)

where M is the matrix of Eq. 13, u is an eigenvector of matrix M, and λis an eigenvalue associated with u. The magnitude of each eigenvalue ofthe matrix M is related to the “significance” of the associatedeigenvector. Stated differently, the eigenvalue indicates how much thecurvature along the associated eigenvector contributes to the localcurvature determined by the matrix M. Accordingly, a in Eq. 13 is theeigenvector associated with the smallest eigenvalue and indicates thedirection in which the change in intensity is the smallest. The largesteigenvalue of the matrix M is associated with the principal direction ofcurvature.

In FIG. 4, the linearly independent eigenvectors u₀ and u₁ (i.e.,eigenvectors u₀ and u₁ are orthogonal) are shown on the illustratedintensity curve. The eigenvalue λ₀ herein denotes the eigenvalue havingthe greatest absolute value and is referred to as the principaleigenvalue. Accordingly, the associated eigenvector u₀ indicates theprincipal direction of curvature at a target pixel and λ₀ is related tothe magnitude of the curvature. The eigenvalue λ₁ (referred to as thesecondary eigenvalue) is related to the magnitude of curvature in thedirection of u₁, i.e., in a direction orthogonal to the principaldirection of curvature indicated by u₀. Along the ridge of the Gaussianprofile (i.e., in the direction u₁), the intensity should besubstantially zero and the change in intensity relatively small and inthe noiseless case is zero (i.e., the intensity does not change as afunction of z in the direction of the centerline). Accordingly, bydetermining the eigenvector associated with the smallest eigenvalue, thedirection a which corresponds to the direction of the centerline may bedetermined. Thus, the orientation of the centerline may be determined ateach of the selected voxels.

Centerline Detection

Having determined scale and orientation for the feature detectionfilter, the feature of interest may be detected. According to someembodiments, centerline detection is performed using a Gaussiancenterline filter. For example, assume the density inside the vesselsatisfies the Gaussian model:

$\begin{matrix}{{I(r)} = {{I_{0}e} - \frac{r^{2}}{2\sigma^{2}}}} & (15)\end{matrix}$

Here, r is in the direction perpendicular to the vessel axis; σ is theradius of the vessel; and I₀ is the intensity at the center. In order todetect a Gaussian vessel, a filter with radial variation correspondingto the 2nd derivative of the Gaussian may be used:

$\begin{matrix}{{h(r)} = {\left( {\frac{r^{2}}{\sigma^{2}} - 1} \right){\mathbb{e}}^{- \frac{r^{2}}{\sigma^{2}}}}} & (16)\end{matrix}$

The application of this filter corresponds to a volume integral overspace. This volume integral should vanish if the filter is embedded inmaterial with constant density. However the 2nd derivative of theGaussian does not, i.e.,

$\begin{matrix}{{\int_{0}^{\infty}{\left( {\frac{r^{2}}{\sigma^{2}} - 1} \right){\mathbb{e}}^{- \frac{r^{2}}{\sigma^{2}}}r{\mathbb{d}r}}} = 1} & (17)\end{matrix}$

This problem can be fixed by adding an offset,

$\begin{matrix}{{\int_{0}^{\infty}{\left( {\frac{r^{2}}{\sigma^{2}} - 2} \right){\mathbb{e}}^{- \frac{r^{2}}{\sigma^{2}}}r{\mathbb{d}r}}} = 0} & (18)\end{matrix}$

Therefore, the centerline filter has the form

$\begin{matrix}{{f(r)} = {{\frac{e}{4{\prod\sigma^{2}}}\left\lbrack {2 - \left\lbrack \frac{r}{\sigma} \right\rbrack^{2}} \right\rbrack}{\mathbb{e}}^{- \frac{r^{2}}{2\sigma^{2}}}}} & (19)\end{matrix}$

This filter has a positive core when r<√{square root over (2)}σr< andnegative shell when r>√{square root over (2)}σ.

Applicant has appreciated that in the presence of noise, a centerlinefilter that closely mimics the shape of a Gaussian as described abovemay at times be inaccurate, especially in situations where vesselstructures are relatively close together. In particular, the continuousdecay of the Gaussian may incorrectly detect or fail to detectcenterline voxels in certain situations, such as when vessel structuresare close together and/or in circumstances where relatively small vesselstructures appear nearby relatively large vessel structures.

Applicant has appreciated that a modified centerline filter may be moreeffective at accurately identifying centerline points, particularly inthe presence of noise. According to some embodiments, centerlinedetection is performed using a filter that better matches the profile ofvessel structures in an image. FIG. 10A illustrates a matched filter inaccordance with some embodiments of the present invention. Filter 900includes an inner core and an outer core. Rather than a Gaussian kernel,filter 900 includes a step function between the inner and outer core. Asa result, the filter support is more compact and the filter is able tomore accurately detect vessel structures that are close together. Inaddition, because the filter better matches vessel profiles, centerlinedetection may be more accurate. An example of values assigned to thematched filter 900 according to some embodiments include:

$\begin{matrix}{{f_{s}\left( {r,z} \right)} = \left\{ \begin{matrix}1 & {r \leq {s\mspace{14mu}{and}\mspace{14mu} z} \leq {\sqrt{2}s}} \\0 & {s < r \leq {\sqrt{2}s\mspace{14mu}{and}\mspace{14mu} z} \leq {\sqrt{2}s}} \\{- 1} & {r > {\sqrt{2}s\mspace{14mu}{or}\mspace{14mu} z} > {\sqrt{2}s}}\end{matrix} \right.} & (20)\end{matrix}$

An illustration of the profile of the above filter along the axis x-x′is shown pictorially in FIG. 10B. As shown, the size of the matchedfilter is based on the scale s detected during scale detection. Applyingthis filter, the centerline response may be given as:r(x,y,z)=∫∫∫T[f(r,z)G(0σ]I(x,y,z)dxdydz  (21)

where G(0, σ) is a Gaussian smooth kernel. When the scale of the filteris small (e.g., when scale detection determines that the local scale isrelatively small), the filter defined by Eq. (20) may not have a zeronet volume (volume of the positive core minus the volume of the negativecore). This may cause detection difficulties because the filter may havenon-zero response when applied to a non-zero uniform background. Asshown in the FIG. 12, when the scale of the filter is small, the netvolume percentage may be quite large. For example, for a centerlinefilter with scale of 1.5, the net volume is 35% of the total volume ofthe filter. Thus, the filter may generate filter bias in the favor ofsmall scale.

Therefore, to address this bias the filter described above may bemodified as:

$\begin{matrix}{{f_{s}\left( {r,z} \right)} = \left\{ {{\begin{matrix}1 & {r \leq {s\mspace{14mu}{and}\mspace{14mu} z} \leq {\sqrt{2}s}} \\0 & {s < r \leq {{\sigma(s)}\mspace{14mu}{and}\mspace{14mu} z} \leq {\sqrt{2}{\sigma(s)}}} \\{- w_{s}} & {r > {{\sigma(s)}\mspace{14mu}{or}\mspace{14mu} z} > {\sqrt{2}{\sigma(s)}}}\end{matrix}{where}},} \right.} & (22) \\{{\sigma(s)} = \left\{ \begin{matrix}{{\sqrt{2}s} + 0.5} & {{{if}\mspace{14mu} s} < 10} \\{\sqrt{2}s} & {otherwise}\end{matrix} \right.} & (23)\end{matrix}$and w_(s) is a function of scale s so that,∫∫∫_(r>σ(s) or z>√{square root over (2)}σ(s)) w _(s) dxdydz=∫∫∫_(r≦a and z≦√{square root over (2)}s) dxdydz  (24)

An illustration of the profile of the filter expressed in Eq. (22) alongthe axis x-x′ is shown pictorially in FIG. 10C. The matched filtersdescribed above may be particularly effective at accurately detectingcenterline voxels in the presence of noise and in circumstances whensubject matter of interest is positioned in close proximity to eachother.

The matched filters described above may be applied to a plurality ofselected voxels in the image. Accordingly, for each selected voxel atwhich the matched filter is applied, there will be an associated filterresponse indicative of the likelihood that the corresponding voxel is acenterline voxel. However, only the maximum filter responses may be ofinterest. That is, the maximum filter responses are those that are mostlikely to be centerline voxels. Accordingly, filter responses that arenot maximum may be suppressed such that only those voxels having maximumfilter responses remain.

Non-Maximum Suppression

In some embodiments, non-maximum suppression may be performed. Forexample, after centerline filtering, each voxel has a response. Theresponse on each voxel indicates how likely it is that the voxel is acenterline voxel. Since the center line voxel should have the maximumresponse in the plane perpendicular to the axis, the purpose ofnon-maximum suppression is to suppress non-maximum responses toeliminate non-centerline voxels. On each voxel, a cutting planeperpendicular to the vessel axis may be used to suppress the non-maximumresponses. On the cutting plane, only local maximums of centerlinefilter responses are kept and all other responses are suppressed.Interpolating the centerline location in order to achieve sub-voxelaccuracy is described below.

In some embodiments, location interpolation on the cutting plane may beperformed. After obtaining the direction of the cylinder, a cuttingplane perpendicular to this direction may be used to apply thenon-maximum suppression as an analog to the traditional computer visionedge detection problem. Given an arbitrary voxel x, the voxel x may betested to determine whether the voxel is a local maxima. According tosome embodiments, the cutting plane may be centered on x and thecenterline response R(x) may be compared with any other responses in itscutting plane neighborhood N(x, v_(x)). That is, the response field inthe neighborhood N (e.g., a 3×3×3 neighborhood) may be projected ontothis cutting plane. If the response at voxel x is larger or equal to allof the responses of neighborhood voxel, voxel x may be labeled as alocal maxima. Otherwise, voxel x is labeled as a non-maxima voxel andsuppressed. This test may be expressed as:

$\begin{matrix}{{{IsMaxima}(x)} = \left\{ \begin{matrix}{true} & {{{R(x)} \geq {R(y)}},{\forall{y \in {{??}\left( {x,v_{x}} \right)}}}} \\{false} & {otherwise}\end{matrix} \right.} & (25)\end{matrix}$

where N(x,vx) denotes the cutting plane neighborhood of the point x.Once the neighborhood is determined, the parabolic function as shownbelow may be used to interpolate the sub-voxel maximum location.r(x,y)=ax ² +by ² +cxy+dx+ey+f  (26)

Given the above response model and the centerline filter responses in asmall region around the center, the following equations may be used:

$\begin{matrix}{\;{{{{an}^{2} + {bm}^{2} + {cmn} + {dn} + {em} + f} = {r\left( {n,m} \right)}}{{{a\left( {n - 1} \right)}^{2} + {bm}^{2} + {{cm}\left( {n - 1} \right)} + {d\left( {n - 1} \right)} + {em} + f} = {r\left( {{n - 1},m} \right)}}\mspace{310mu}{\vdots\mspace{281mu}\vdots}{{{a\left( {n - 1} \right)}^{2} + {bm}^{2} + {{cm}\left( {n - 1} \right)} - {d\left( {n - 1} \right)} - {em} + f} = {r\left( {{1 - n},{- m}} \right)}}\mspace{191mu}{{{an}^{2} + {bm}^{2} + {cmn} - {dn} - {em} + f} = {r\left( {{- n},{- m}} \right)}}}\mspace{169mu}} & (27)\end{matrix}$

This linear form can be written as a matrix form

$\begin{matrix}{{A\begin{bmatrix}a \\b \\c \\d \\e \\f\end{bmatrix}} = \begin{bmatrix}{r\left( {n,m} \right)} \\{r\left( {{n - 1},m} \right)} \\\vdots \\{r\left( {{1 - n},{- m}} \right)} \\{r\left( {{- n},{- m}} \right)}\end{bmatrix}} & (28) \\{{{where}\mspace{14mu} A} = \begin{bmatrix}n^{2} & m^{2} & {mn} & n & m & 1 \\\left( {n - 1} \right)^{2} & m & {m\left( {n - 1} \right)} & {n - 1} & m & 1 \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\n^{2} & m^{2} & {m\left( {n - 1} \right)} & {1 - n} & {- m} & 1 \\n^{2} & m^{2} & {mn} & {- n} & {- m} & 1\end{bmatrix}} & (29)\end{matrix}$

The maximum location is determined by the stationary condition

$\frac{\partial r}{\partial x} = {\frac{\partial r}{\partial y} = 0.}$That is,2ax+cy _(—) d=0cx+2by+e=0  (30)Therefore,

$\begin{matrix}\begin{matrix}{\begin{bmatrix}x \\y\end{bmatrix} = {- {\begin{bmatrix}{2a} & c \\c & {2b}\end{bmatrix}^{- 1}\begin{bmatrix}d \\e\end{bmatrix}}}} \\{= {{\frac{1}{{4{ab}} - c^{2}}\begin{bmatrix}{{- 2}b} & c \\c & {{- 2}a}\end{bmatrix}}\begin{bmatrix}d \\e\end{bmatrix}}} \\{= \begin{bmatrix}\frac{{ce} - {2{bd}}}{{4{ab}} - c^{2}} \\\frac{{cd} - {2{ae}}}{{4{ab}} - c^{2}}\end{bmatrix}}\end{matrix} & (31)\end{matrix}$

In some embodiments, the size of the neighborhood N(x, vx) is determinedbased characteristics of the image in the neighborhood. There is anatural question of how big the neighborhood size should be chosen inthe non-maximum suppression algorithm. In some embodiments, the smallestsize of 3×3×3 may be used, but this choice may cause outliers to survivenon-maximal suppression in noisy regions. An alternative method ofchoosing the parameter is to use the results from radius and/or scaledetection. In some embodiments, to avoid suppressing real vessels whichare close to each other, a conservative approach may be used whenchoosing the neighborhood:

$\begin{matrix}{n = {{2\left\lfloor \frac{s}{\sqrt{2}} \right\rfloor} = 1}} & (32)\end{matrix}$

It should be appreciated that the neighborhood in Eq. (32) is exemplaryand an adaptive neighborhood, for example, based on scale may bedetermined in other ways, as the aspects of the invention are notlimited in this respect.

Linking

As discussed above, the output from centerline filtering and non-maximumsuppression processes provides a 3D field in which each point is markedas either belonging to or not belonging to a centerline. In someembodiments, centerline points can be associated with other informationsuch as radius, strength and orientation of the cylinder element (e.g.,using the Poker Chip representation). The task of cylinder elementlinking may include connecting centerline points and identifying thejunctions to generate a vessel network. In some embodiments, practicaldifficulties may arise associated with one or more of the following: 1)small pieces of centerline may be missing; 2) due to digitization, thecenterline segments after non-maximum suppression form “zig-zags.” 3)small outlier centerline segments may appear to be present due to noisewhere there is no real centerline; and 4) junction region may confusethe linking algorithm and lead to wrong linkages. Applicant hasdeveloped a linking method that addresses one or more of thesedifficulties.

In some embodiments, a local cylinder element linking algorithm may beused as follows: 1) start with a most prominent cylinder segment; 2)search in front of the cylinder segment until no more directly connectedsuccessors exist; 3) search behind the cylinder segment until no morepredecessors exist; 4) mark all the connected cylinder elements; and 5)repeat the above steps until no more cylinder segments are leftunmarked. An example of a linking method according to some embodiments,is described in further detail below.

A single branch of a vessel may be modeled as a digitization of asmooth, 3D curve which connects all the poker chips that belong to thisbranch. Given a point y that has already been selected as part of abranch (e.g., a centerline point with a large response), point y islinked to a nearby point based on a given criteria. For example, linkingmay be selected to prefer connecting to a point which is close to pointy (distance), that does not require a large change in the expecteddirection v_(y) (direction), and that has a response that is as similarto the response at point y as possible (response). Each candidate pointx may be subjected to this criteria to determine which candidate is themost likely link.

According to some embodiments, the criteria is determined using aprobabilistic model. For example, the above tests may be performed byfinding the point x which maximizes the posterior possibility,Pr(L _(y) =x|x,v _(x) ,r _(z))  (33)

Without knowing the prior information, maximizing the posteriorprobability is the same as maximizing the likelihood,Pr(x,v _(x) ,r _(x) |L=x)  (34)

If the tests of the distance, direction and response are conditionalindependent given L_(y)=x, it may be sufficient to provide marginaldistribution for each tests.

$\begin{matrix}\begin{matrix}{{\Pr\left( {x,v_{x},{{R_{x}❘L_{y}} = x}} \right)} = {\Pr\left( {{{dist}\left( {x,y} \right)},\overset{\longrightarrow}{xy},{{R_{y}❘L_{y}} = x}} \right)}} \\{= {\Pr\left( {{{{dist}\left( {x,y} \right)}❘{L_{y}\left( {x,y} \right)}},\overset{\longrightarrow}{xy}} \right)}} \\{{\Pr\left( {\overset{\longrightarrow}{xy}❘{L\left( {x,y} \right)}} \right)}{\Pr\left( {r_{y}❘{L\left( {x,y} \right)}} \right)}} \\{= {{\Pr\left( {{{dist}\left( {x,y} \right)}❘x} \right)}{\Pr\left( {\overset{\longrightarrow}{xy}❘v_{x}} \right)}}} \\{{\Pr\left( {R_{y},{s_{x}❘R_{x}},s_{y}} \right)}\mspace{14mu}(7)}\end{matrix} & (35)\end{matrix}$

Among the three tests defined above, Applicant has determined thatdistance tends to be the most reliable. Therefore, it is possible tobuild a probability model for this distance test. According to someembodiments, a Gaussian model is chosen for the distance test topenalize the distance between point y and candidate x exponentially:

$\begin{matrix}{{\Pr\left( {{{dist}\left( {x,y} \right)}❘x} \right)} = {\frac{1}{\sqrt{2\pi}}{\exp\left( {- \frac{{{x - y}}^{2}}{2}} \right)}}} & (36)\end{matrix}$

As discussed above, another useful test is determining the extent ofdirection change in the linked centerline points (e.g., as determinedfrom orientation detection) that would be incurred by linking point ywith candidate point x. However, Applicant has appreciated that thedirection of the centerline from the orientation detection may zig-zaglocally due to digitization. Therefore, relying entirely on thedirection obtained from the orientation detection may lead to linkingerrors. To address this difficulty, some embodiments employ a superGaussian model to test the possibility of connecting point y withcandidate x, given the centerline direction of point x.

$\begin{matrix}{{\Pr\left( {\overset{\longrightarrow}{xy}❘v_{x}} \right)} = {\frac{1}{Z}{\exp\left( {- \frac{{\theta\left( {\overset{\longrightarrow}{xy},v_{x}} \right)}^{4}}{\sigma^{4}}} \right)}}} & (37)\end{matrix}$

The super Gaussian model has a flat top which allows the test totolerate relatively large angle variation. As discussed above, thecenterline response and scale may also be used to test the viability oflinking point y with candidate x. It is reasonable to assume that thecenterline responses and scale are smoothly changing along a singlebranch. In the other words, linking to a point which causes centerlineto rapidly change may be assigned a low probability. With thisintuition, a response test model may be constructed as follows:

$\begin{matrix}\begin{matrix}{{\Pr\left( {R_{y},{s_{y}❘R_{x}},s_{x}} \right)} = {{\Pr\left( {{s_{y}❘R_{x}},s_{x}} \right)}{\Pr\left( {{R_{y}❘R_{x}},s_{x},s_{y}} \right)}}} \\{= {{\Pr\left( {s_{y}❘s_{x}} \right)}{\Pr\left( {{R_{y}❘s_{y}},R_{x},s_{x}} \right)}}} \\{= {\frac{1}{Z}{\exp\left( {- \frac{\left( {s - s_{x}} \right)^{2}}{2{\sigma_{s}^{2}(s)}}} \right)}{\exp\left( {- \frac{\left( {\frac{R_{y}}{s_{y}^{3}} - \frac{R_{x}}{s_{x}^{3}}} \right)^{2}}{2\sigma_{r}^{2}}} \right)}}}\end{matrix} & (38)\end{matrix}$

where Z is the normalization factor, σ_(s)(s)=max {0.5, 0.2s}. Thus, theabove test may be employed in connection with the algorithm describedabove to link the centerline points (e.g., the centerline points thatsurvived non-maximum suppression). Due to errors in the directionfinder, and grid discretization, some non-centerline points survive fromnon-maximum suppression. However, the number of those points may bereduced by applying an occupancy constraint. The occupancy constraintsoperate on the notion that if a local space is occupied by a previouslylinked branch, then it is not likely possible to be the center ofanother branch. In the other words, a high confidence may be assigned tolong branches to suppress weak branches, if the weak branch occupies thesame space as the strong branch.

As a result of linking the centerline points together, each of whichrepresents a poker chip having a center location (the centerline point),a radius and a direction of the centerline at the center location,further geometry of the vessel may be computed. Referring back to theschematic of the Poker Chip representation in FIG. 2. Having computedeach of the center location c_(i), the radius r and the orientation a,and having linked the adjacent poker chips, additional geometry of theblood vessels may be determined. For example, the linked orientationparameters capture information about the geometry of the centerline. Forexample, by integrating the orientation vectors, the centerline curvemay be obtained. That is, because the orientation vectors represent thetangents of the centerline curve at each location c_(i), the centerlinecurve may be recovered from linked tangents by integrating over somedesired segment of poker chips.

In addition, the linked poker chips may be used to determine higherorder and/or more sophisticated geometrical properties. For example,derivatives of the linked orientation vectors may be used to determinethe curvature of the vessel. The centerline curve, length of the curveand curvature parameters may be used to determine various tortuosityparameters, which may be used to characterize the vessels. Moreover, thePoker Chip representation carries distribution information withrespective to the density of vessel material, the relative distributionof vessels at different radii, etc. These geometrical, structural anddistribution parameters may be used in a number of ways to analyzevasculature, as discussed in further detail below. FIG. 13 illustrates ageometrical representation of vasculature using the linked Poker Chiprepresentation, wherein the geometry was extracted from a 3D volumetricimage using the methods described herein.

According to some embodiments, the linking algorithm may be performed inparallel. Since linking is generally local and may not need to rely onthe information from far away voxels, the algorithm can be parallelizedby dividing the image into small blocks. Then individual CPUs mayoperate on a single block without the need to communicate with otherblocks. Because of the computation requires some neighborhoodinformation, each block may include a fixed margin overlapping with itsneighbor's margin. The speed gained by parallelization is the number ofprocessors divided by one plus overhead caused by margin. In oneexample, dividing a volume of 2000×2000×1400 into 500×500×500 blocks andusing 8 processors produced a gain of 4.49 times processing speed.

The margin for parallelization may be chosen based on the following: 1)the margin for the scale selection m_(s)=r_(max)+1; 2) the margin forthe smoothing m_(sm)=3σ; 3) the margin for the gradient computationmg=1; 4) the margin for the direction detectionm_(d)=m_(g)+r_(max)+1+m_(sm); 5) the margin for centerline filteringm_(c)=max {2r_(max), m_(d)}; and 6) the margin for the non-maximumsuppression m_(spr)=r_(max)+m_(c).

Because the block algorithm for parallelization needs to divide thevolume into blocks at beginning and assembling the blocks into a volumeat the end, away to transform between global coordinates and blockcoordinates may be needed. The block id (b_(x), b_(y), b_(z)) for apoint (i, j, k) in the global coordinate is given as:

$\begin{matrix}{{b_{x} = \left\lfloor \frac{i}{s} \right\rfloor}{b_{y} = \left\lfloor \frac{j}{s} \right\rfloor}{b_{z} = \left\lfloor \frac{k}{s} \right\rfloor}} & (39)\end{matrix}$

The local coordinates in its block is (i′, j′, k′)i′=i−b _(z) sj′=j−b _(y) sk′=k−b _(z) s  (40)

The dimension (s_(x), s_(y), s_(z)) of the block (k_(x), b_(y), b_(z))is:

$\begin{matrix}{{s_{x}\left( b_{x} \right)} = \left\{ {{\begin{matrix}{{mod}\left( {N_{x},s} \right)} & {{{if}\mspace{14mu} b_{x}} = {{\left\lfloor N_{x} \right\rfloor - 1} ⩓ {\left\lfloor \frac{N_{x}}{s} \right\rfloor \neq 0}}} \\0 & {{{if}\mspace{14mu} b_{x}} < 0} \\s & {otherwise}\end{matrix}{s_{y}\left( b_{y} \right)}} = \left\{ {{\begin{matrix}{{mod}\left( {N_{y},s} \right)} & {{{if}\mspace{14mu} b_{y}} = {{\left\lfloor \frac{N_{y}}{s} \right\rfloor - 1} ⩓ {\left\lfloor \frac{N_{x}}{s} \right\rfloor \neq 0}}} \\0 & {{{if}\mspace{14mu} b_{y}} < 0} \\s & {otherwise}\end{matrix}{s_{z}\left( b_{z} \right)}} = \left\{ \begin{matrix}{{mod}\left( {N_{y},s} \right)} & {{{if}\mspace{14mu} b_{z}} = {{\left\lfloor \frac{N_{z}}{s} \right\rfloor - 1} ⩓ {\left\lfloor \frac{N_{x}}{s} \right\rfloor \neq 0}}} \\0 & {{{if}\mspace{14mu} b_{z}} < 0} \\s & {otherwise}\end{matrix} \right.} \right.} \right.} & (41)\end{matrix}$

Given a point (i′, j′, k′) at block (b_(x), b_(y), b_(z)), the globaloffset in the file is:

            (42)${pos} = {{i^{\prime}s_{y}s_{z}} + {j^{\prime}s_{z}} + k^{\prime} + \left( {\quad\underset{\underset{{block}\mspace{14mu}{offset}}{︸}}{{b_{z}N_{x}N_{y}{s_{z}\left( {b_{z} - 1} \right)}} + {b_{y}N_{x}{s_{y}\left( {b_{y} - 1} \right)}{s_{z}\left( b_{z} \right)}} + {b_{x}{s_{x}\left( {b_{x} - 1} \right)}{s_{y}\left( b_{y} \right)}{s_{z}\left( b_{z} \right)}}}\quad} \right)}$

The number of blocks in the x dimension is

${n_{bx} = \left\lceil \frac{N_{x}}{s} \right\rceil},$the number of block in the y dimension is

$n_{by} = \left\lceil \frac{N_{y}}{s} \right\rceil$and the number of blocks in the z dimension is

$n_{bz} = {\left\lceil \frac{N_{z}}{s} \right\rceil.}$A one dimensional block ID1=(1, . . . , n_(bx)n_(by)n_(bz)) to 3D index

$\begin{matrix}{{b_{x} = \left\lfloor \frac{l}{n_{by}n_{bz}} \right\rfloor}{b_{y} = {{\left\lfloor \frac{l - {b_{x}n_{by}n_{bz}}}{n_{bz}} \right\rfloor b_{z}} = {l - {b_{y}n_{bz}} - {b_{x}n_{by}n_{bz}}}}}} & (43)\end{matrix}$Three dimensional block ID (b_(x), b_(y), b_(z)) to one dimensionalblock ID.

As discussed above, the linked Poker Chip representation may be used todetermine a number of geometrical and structural parameters of thevasculature, and also may be used to determine distribution informationof the vasculature. Provided herein is a description of methods thatutilize the extracted geometry to analyze the vasculature fordiagnostic, treatment efficacy assessment, therapeutic, and otherapplications, or any combination thereof.

Information relating to the geometry of a subject's vasculature, or aportion thereof, can be used to determine one or more qualitative and/orquantitative measures of geometrical, structural, and/or distributionparameters of the subject's vasculature that are informative fordiagnostic, predictive, prognostic, therapeutic, interventional,research and/or development purposes, as well as for grading and/orstaging a disease. It should be appreciated that vasculature geometrymay be obtained for any suitable blood vessel volume, as the inventionis not limited in this respect. In some embodiments, all the geometricalinformation captured by the linked Poker Chips within a target volume ofinterest may be evaluated. However, in some embodiments, usefulinformation may be obtained from analyzing only a subset of Poker Chipswithin a target volume (e.g., about 10%, about 20%, about 30%, about40%, about 50%, about 60%, about 70%, about 80%, or about 90%) as theinvention is not limited in this respect.

According to aspects of the invention, the types of geometrical orstructural information that may be extracted from images (e.g.,extracted from a linked Poker Chip representation) includes a measure ofvessel curvature, tortuosity, branching, diameter, etc., or anycombination thereof. Optionally, or additionally, a measure of vesseldensity (and/or the density of vessels having one or more predeterminedstructural characteristics) may be determined and/or analyzed. It shouldbe appreciated that a Poker Chip may consist of or include informationrelating to the size (radius), angle, etc. of the vessels beingrepresented. In some embodiments, the Poker Chip representation mayinclude linking information (e.g., relating to the linkage angle etc.between a first Poker Chip and one or more adjacent Poker Chips).

Tubular structures (e.g., blood vessels in a cast or in vivo) ofdifferent size ranges may be analyzed separately and compared todifferent threshold or reference values as described herein. In someembodiments, one or more structural parameters are obtained (e.g.,calculated or modeled, etc.) for only a subset of size ranges (e.g.,only for those size ranges for which changes are known to be associatedwith a diagnostic, prognostic, clinical, or research application ofinterest). However, in certain embodiments, all of the size ranges areanalyzed. In some embodiments, one or more different parameters areanalyzed for different size ranges. However, in certain embodiments, thesame parameter(s) is/are analyzed for all of the size ranges that arebeing assayed. Analyses may be provided in the form of histograms orcurves representing a distribution of numerical values or scoresobtained for the different ranges.

It should be appreciated that analytical techniques used to categorizeblood vessels based on size may be used to categorize other tubular bodystructures based on size. In some embodiments, once the tubularstructures (e.g., blood vessels) are categorized based on size, theassociated values or scores obtained for different parameters ofinterest can also be categorized and analyzed. Aspects of the inventionmay be automated, for example, as described herein.

Aspects of the invention relate to analyzing data obtained for bodystructures in animals (e.g., in test animals). In one embodiment, theinvention relates to obtaining pattern information relating to one ormore aspects or regions of the vasculature of an animal. Patterninformation obtained according to aspects of the invention may be usedto analyze a disease model (e.g., to assess whether an animal diseasemodel is representative of an actual disease based on structuralvascular features, or to assess the progression of one or more vascularchanges in a test animal that provides a validated disease model, etc.),to evaluate the effectiveness of a treatment regimen, to identifycandidate compounds or treatment regimens that are therapeuticallyeffective, or for other applications where data relating to vascularstructures (e.g., the progression of vascular structures, changes invascular structure over time or in response to different drugs or drugdosages or administration frequencies, etc., or any combination thereof)is informative. For example, aspects of the invention may be used toidentify one or more pattern elements that can be used to help diagnoseor evaluate diseases, provide prognostic information, monitortreatments, screen therapeutic agents, select one or more therapeuticagents (e.g., help determine or predict a subject's responsiveness to aparticular drug), etc., or any combination thereof.

Aspects of the invention may be used to study, identify, and or analyzegeometrical, structural, and/or distributional features of blood vesselsthat are associated with one or more diseases or conditions representedby an animal of interest. In some embodiments, an animal may be adisease model as described herein. In some embodiments, an animal may beundergoing a therapeutic regimen of interest. In some embodiments, ananimal may be treated with a candidate therapeutic compound.Accordingly, aspects of the invention may be used to identify, analyze,and/or evaluate one or more vascular patterns or changes in vascularpatterns associated with a disease. Aspects of the invention also may beused to evaluate the effects of one or more therapeutic regimens orcandidate compounds. In some embodiments, therapeutic effectiveness maybe evaluated using one or more vascular patterns or changes therein as amarker of a response (or lack thereof) to treatment. Accordingly,aspects of the invention may be used to identify particular vascularpatterns that are indicative of certain diseases or disease stages.These patterns can subsequently be used in sensitive assays to detectdiseases in vivo (e.g., in human subjects). Other aspects of theinvention may be used to select therapeutic regimens or candidatecompounds for administration to a patient (e.g., a human patient) in atherapeutically effective amount and in a physiologically acceptableform.

It should be appreciated that in some embodiments, an animal (e.g., ananimal that is perfused with a casting agent composition) may besacrificed prior to analysis regardless of whether the analysis isperformed in situ or not. Accordingly, in some embodiments, changes overtime may be studied using a plurality of animals and using one or moreanimals for each time point of interest. In some embodiments, differentdosages, different therapeutic regimens, different drugs or drugcombinations, or any combination of two or more thereof may be studiedusing different animals (with at least one animal for each condition ofinterest). It should be appreciated that combinations of time coursesand drugs, drugs dosages, or other therapeutic regimens similarly may bestudied using a plurality of different animals, each representing aunique condition. It should be appreciated that the different animalsare preferably genetically identical or similar (e.g., identical for atleast one trait that is associated with a disease or condition ofinterest). In some embodiments, the animals may be mice, rats, sheep,cats, dogs, primates, or any suitable non-human experimental animal.

In some embodiments, a combination of different drugs, different doses,etc., may be evaluated at a series of time points according to aspectsof the invention. Again, it should be appreciated that a differentanimal may represent a different drug, dosage, time point, orcombination thereof, because each animal may be sacrificed for analysis.However, in some embodiments, a single animal may be tested at differentsites (representing, e.g., different drugs, dosages, time points, etc.)depending on the impact of the casting agent that is used and the siteof administration of the casting agent.

In some embodiments, samples from one or more animals may be preparedand analyzed periodically during the time course of a treatment (e.g.,using a group of animals exposed to the same experimental conditions).In some embodiments, different conditions may be compared. For example,separate groups of animals (e.g., groups of mice) may be exposed to acandidate drug and a placebo (or other control). In some embodiments,subsets of animals (e.g., one or more animals) may be perfused with acasting agent composition at different time points and vascularstructures may be imaged (e.g., directly or through reconstruction) foreach time point. For example, tumors may be induced ingenetically-altered mice using appropriate controls and different doselevels or regimens (e.g., 1, 2, 3, 4, 5, or more different dose levelsor regimens) of one or more therapeutic compounds or compositions.Vascular structures then may be analyzed at different time points usingmethods of the invention to evaluate the effectiveness of a drugcomposition and/or to identify biological markers that can be used tomonitor a patient response to the drug composition. It should beappreciated that vascular structures of different sizes may be studiedto identify structural features and/or distribution patterns ofinterest. In some embodiments, blood vessels having a diameter of about50 microns are studied. However, it should be appreciated that smalleror larger vessels, or a combination thereof, may be studied.

In some embodiments, a vasculature characteristic may be evaluated overtime by comparing results at different time points. However, it shouldbe appreciated that the end-point of a study may be used as a singletime point and characteristics associated with different diseases ortreatments may be compared to identify or infer changes associated witha disease, treatment, or other condition of interest. Aspects of theinvention can be used to analyze data obtained from any suitable imagesource to identify one or more patterns associated with tubularstructures of different sizes (e.g., structural patterns of bloodmicro-vessels). One or more parameters of a structural pattern can beused as biomarkers for different biological conditions and processes(including pathogenic conditions). Accordingly, aspects of the inventionrelate to disease detection, diagnosis, grading, staging, diseasemonitoring, monitoring the effectiveness of therapy and interventionalapplications based on an analysis of structures (e.g., in situstructures) to identify patterns that may be associated or correlatedwith a disease or other physiological condition. According to theinvention, a pattern may comprise one or more different parameters.Parameters may be one or more structural features of individual tubularstructures and/or one or more distribution properties (e.g., spatialdistribution, spatial orientation, frequency, number, etc., or anycombination thereof) of one or more tubular structures and/or one ormore distribution properties (e.g., spatial distribution, spatialorientation, frequency, number, etc., or any combination thereof) of oneor more individual tubular structural features within a subject or awithin a region of interest in the subject, or any combination thereof.Accordingly, a vasculature pattern may include one or more structuralfeatures of an individual blood vessel (e.g., micro-vessels), adistribution of one or more blood vessels (e.g., micro-vessels) within asubject, a distribution of one or more individual blood vesselstructural features (e.g., individual micro-vessel structural features),or any combination thereof. An individual blood vessel structuralfeature may include, but is not limited to, vessel tortuosity,curvature, branching (e.g., frequency, angle, hierarchy, etc.),diameter, direction, etc., or any change (e.g., variation or frequency)of any of these features over a predetermined length of the blood vesselbeing analyzed, or any combination thereof. A distribution of bloodvessels or individual blood vessel structural features may include, butis not limited to, a blood vessel density, a distribution of bloodvessel directions, a distribution of blood vessel diameters, adistribution of distances between blood vessels, a distribution of bloodvessel spatial orientations (e.g., relative to each other), adistribution of blood vessel curvatures, a distribution of any otherindividual blood vessel structural features described herein, otherdistributions of blood vessel parameters or any combination of two ormore thereof. It should be appreciated that the distribution of bloodvessels or blood vessel structural features may be determined and/oranalyzed for a predetermined region within a subject (e.g., a targetvolume of tissue within a subject) or within predetermined tissues ororgans within a subject or throughout the subject (e.g., within avascular cast). It also should be appreciated that either the absence orpresence of blood vessels or of individual blood vessel structuralfeatures within a predetermined volume being analyzed may be a patternparameter that can be used in analytical methods of the invention. Italso should be appreciated that one or more pattern parameters may bemonitored and/or analyzed as a function of time. Accordingly, bloodvessel patterns can be used as biomarkers for different biologicalconditions and processes (including pathogenic conditions). Accordingly,aspects of the invention relate to identifying and evaluating biologicalmarkers that may be used for in vivo disease detection, diagnosis,grading, staging, for disease monitoring, for monitoring theeffectiveness of therapy and interventional applications in liveanimals, including humans, based on an analysis of vasculature patternsincluding vasculature morphology and/or architecture in experimentalsubjects, for example experimental animals (e.g., animals perfused withone or more casting agent compositions). In one embodiment, the in vivodensity, and/or diameter distribution, and/or geometric orientation ofblood vessels (e.g., micro-vessels) may be analyzed, quantified, and/orevaluated for disease detection, monitoring, and/or interventionalapplications. In one embodiment, the sensitivity and specificity ofdisease diagnosis may be enhanced by analyzing and evaluating in vivovasculature morphology and/or architecture associated with a tissuelesion. Accordingly, aspects of the invention include detecting in vivoindicia of diseases associated with abnormal vascular structures orpatterns. Other aspects include disease diagnosis, staging, grading,monitoring and prognosis, patient treatment, drug development andvalidation, and research applications. It should be appreciated that oneor more biological markers identified in vascular casts in associationwith a response to a known drug or treatment may be used as a referencemarkers to evaluate the effectiveness of additional drugs or treatmentsin comparison to the known drug or treatment.

Certain embodiments according to the present invention includes a methodof analyzing geometric features of blood vessels and correlating one ormore features with a biological process, condition, or disease.Accordingly, certain geometric features of blood vessels may be used asbiomarkers indicative of particular biological processes, conditions,and/or diseases.

In some embodiments, data for tubular structures (e.g., blood vessels)may been sorted into bins based on their size (e.g., their diameter).Aspects of the invention may increase the analytical resolution whenevaluating structural information that is obtained for one or moreexperimental models and/or subjects being evaluated. According toaspects of the invention, a binned structural analysis refers to anyanalysis of tubular structures that have been sorted or categorizedaccording to size (e.g., according to the diameter or radius of thetubular structure in an area of interest). For example, in someembodiments a binned micro-vessel density (BMVD) analysis refers to ananalysis of blood vessel density based on blood vessels that have beencategorized according to vessel diameter in an area of interest.

Binned analytical techniques can be applied to the analysis of manydifferent parameters that may be characteristic of tubular structures.Binned analytical techniques may be performed on tubular structuresobserved in casts or in vivo (e.g., in situ). For example, bins oftubular structures having different diameters can be evaluated todetermine one or more of the following parameters: tortuosity,curvature, density, branching frequency, branching hierarchy (e.g.,presence or absence of a branching hierarchy), relative distributionand/or direction of tubular structures (e.g., blood vessels), etc., orany combination thereof. By performing the analysis on binned data,small changes that primarily affect structures in one size range aremore likely to be detected, because they are not masked by a relativeabsence of change in structures in other size ranges. Accordingly,methods of the invention can be used to refine an analysis of tubularstructures (e.g., blood vessels) over time or in response to disease ortreatment, etc., where the analysis may be performed on casts and/or invivo. Aspects of the invention can also be used to detect or delineatediseased tissue (e.g., cancerous or pre-cancerous tissue, necroticregions, etc.) in casts and/or in vivo.

It should be appreciated that, regardless of the source of informationrelating to vessel geometry, structure, and/or distribution (e.g., fromanalysis of BMVD, casts, in vivo, images, representations, etc., or anycombination thereof), analytical methods described herein may be used.Accordingly, any analytical descriptions of vessel distributions thatare provided in the context of one source of information may be appliedto that analysis of vessel distributions obtained from one or more othersources as appropriate.

In some embodiments, spatiotemporal information about the vesseldistribution provides numerous indicators about the health of a tumor,the effectiveness of a treatment such as the efficacy of a particularanti-angiogenic drug, and how a tumor is changing over time with respectto differently sized vessels. Numerous exemplary applications using oneor more distribution analyses (e.g., based on BMVD measurements), inaccordance with various aspects of the present invention are describedherein. Applicant has identified and disclosed various applications thatare facilitated by the acquisition of information about vesselcharacteristics, distribution, size, shape, etc., in PCT applicationUS2005/047081 filed on Dec. 22, 2005, which is hereby incorporated byreference in its entirety. Applicant has appreciated that certain ofthese applications are facilitated by obtaining one or more BMVDmeasurements or by using one or more alternative binned analyses. Itshould be appreciated that any application may involve an analysislimited to one or more (e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, or more) binsof microvasculature of different sizes. For example, binned analyses maybe useful for diagnostic applications. In one embodiment, aspects of theinvention can be used to detect and diagnose diseases associated withpatterns (e.g., individual structural features or distributions) of insitu tubular networks. In some cases, a diagnosis can be rendered froman examination of the patterns (e.g., individual structural features ordistributions) of interest at a single time. Alternatively, diseaseprogression in a subject can be tracked by performing a structuralanalysis at two or more (e.g., 3, 4, 5, 6, 7, 8, 9, 10, or more) timepoints. Disease tracking can be used to provide diagnostic andprognostic information for a patient. For example, disease progressioninformation can be used to assess the aggressiveness and/or invasivenessof a tumor.

The invention can be used to screen an individual or a population forthe presence of indicia relating to one or more diseases. As mentionedherein, the screen may be a whole body screen, or may be focused on oneor more target regions (e.g., specific organs or tissues).

In one embodiment, the techniques described herein can be usedautomatically to identify individuals with one or moredisease-associated structural patterns or features. These individualscan be subsequently tested for additional indicia of disease. Thesubsequent testing can take any suitable form, as the aspects of thepresent invention described herein are not limited in this respect. Forexample, follow on testing can employ conventional techniques. As anon-limiting example, the use of aspects of the present invention mayenable cost-effective screening techniques that may identify arelatively small pool of candidates as at risk of a disease, and mayjustify the use of relatively more expensive testing procedures to reacha final diagnosis or prognosis, wherein the follow on techniques may betoo expensive to administer to a wider sample that has not been narrowedusing the techniques of the present invention described herein. As afurther example, aspects of the present invention described herein,either alone or in combination with other techniques, can be used toperform subsequent tests. In this respect, the sensitivity of theinitial screening can be set relatively high, such that it may indicatesome false positives, and subsequent application of techniques inaccordance with aspects of the present invention described herein can beemployed with a higher degree of sensitivity that may provide moredetailed information.

In one embodiment, aspects of the present invention can be used toscreen a population of at risk individuals (e.g., individuals withgenetic or other risk factors for a disease such as cancer, acirculatory disorder, or other disease) to identify the presence ofdisease indicia in one or more individuals.

In one embodiment, diagnostic methods of the invention arecomputer-implemented to increase efficiency and throughput, and reducevariability associated with individual physicians. However, as discussedherein, in some embodiments, the final diagnosis may be made by aphysician based on information generated by an automated analysis or astructural representation using aspects of the invention describedherein.

As shall be appreciated from the foregoing, aspects of the invention canbe used on patients known to have a disease, or can be used to screenhealthy subjects on a regular basis. A subject can be screened for oneor more diseases. Screening can be done on a regular basis (e.g.,weekly, monthly, annually, or other time interval); or as a one timeevent. Different conditions can be screened for at different timeintervals and in function of different risk factors (e.g., age, weight,gender, history of smoking, family history, genetic risks, exposure totoxins and/or carcinogens etc., or a combination thereof).

In one embodiment, aspects of the invention can be employed to diagnose,evaluate or stage diseases associated with changes in vasculaturestructure. The detection of small changes in vasculature structure maybe informative for early stage disease detection and disease monitoring.A morphological determination of binned blood vessels may be analyzedand one or more patterns (e.g., individual structural features ordistributions) may be evaluated for the presence of abnormal properties.In one embodiment, a vasculature structure may be obtained including aseries of interconnected branched blood vessels and may includearteries, arterioles, veins, venules, capillaries, and other sized bloodvessels. However, according to aspects of the invention, aninterconnected vasculature structure is not required and different sizesof blood vessels can be analyzed separately and represented on ahistogram or other form of distribution representation. In some aspectsof the invention, blood vessels of the entire body can be analyzed, andin other aspects the blood vessels of a target organ, tissue, or partthereof can be analyzed. In some aspects of the invention, only a subsetof blood vessel sizes is binned and analyzed (e.g., blood vessels with adiameter below about 500 microns, preferably below about 200 microns,more preferably below 100 microns, even more preferably below 50microns, and even more preferably below 25 microns). In one embodiment,only capillary blood vessels are analyzed. In another embodiment,capillaries and small arteries and veins (e.g., arterioles and venules)are analyzed. For example, an arborescent vasculature can be analyzed inany tissue where it is found (e.g., an arborescent mucosal vasculaturesuch as the oesophageal arborescent mucosal vasculature).

The branches of a vascular tree may be analyzed to glean informationabout the status of the patient. In one embodiment, the branches of avascular tree may be followed to identify specific regions where certaincharacteristics of angiogenesis may be evaluated (e.g., start with alarge branch and follow the tree to second, third, or fourth, orsubsequent levels of branching to identify small blood vessels that mayhave abnormal structures if they are providing a blood supply associatedwith a disease). Alternatively, several different blood vessel sizes inthe vascular tree may be evaluated for signs of angiogenesis. In anotherembodiment, the overall branching pattern of a vascular tree can beanalyzed. For example, a healthy vascular tree may be approximatelyhierarchical in that the size of the blood vessels generally decreasesas the vessels branch. In contrast, a diseased (e.g., angiogenic)vascular tree may be less hierarchical with areas of significant bloodvessel branching with little or no decrease in blood vessel size. Itshould be appreciated that the nature and extent of the analysis maydepend on the goal of the diagnostic evaluation. For example, a fullbody scan can be evaluated selecting all vascular structures andanalyzing the entire vascular network for signs of different diseases.Alternatively, a region of a body suspected of being diseased may beselected and the data may be processed to focus on the vasculature inthat region (e.g., to obtain a segmented representation of structures inthe region of interest). A region of interest may be an organ (e.g.,pancreas, liver, breast, colon etc.) or a tissue (e.g., skin epidermaltissue). The presence of an abnormal vasculature structure can be anearly indication of a range of diseases for which early detection iscritical for effective treatment.

Diseases associated with changes in vascular structure (e.g., that canbe detected by the presence of abnormal vascular patterns at a giventime or abnormal structural changes observed as a function of time)include, but are not limited to, cancer, heart diseases and relatedcirculatory disorders, eye diseases, skin disorders, and surgicalconditions. For example, diseases and conditions associated with changesin vascular structure include, but are not limited to, tumorangiogenesis, recurrent and progressive cancers, coronary arterydisease, cardiomyopathy, myocardial ischemia, arteriosclerosis,atherosclerosis, atherosclerotic plaque neovascularization, arterialocclusive disease, ischemia, ischemic or post-myocardial ischemiarevascularization, peripheral vascular disease (including diabeticretinopathy), thromboembolic diseases (e.g., stroke, pulmonary embolism,brain aneurisms, and deep venous thrombosis), claudication,rheumatologic disorders (e.g., arthritis), immune disorders (e.g.,rheumatoid arthritis, vasculitis, Wegner's granulomatosis, and systemiclupus erythematosis (SLE)), pulmonary disorders (including, emphysema,COPD, idiopathic pulmonary fibrosis, pulmonary arterial hypertension,and other respiratory disorders), myeloma, vascular proliferativedisorders, gastrointestinal disorders (e.g., Crohn's disease, ulcerativecolitis, and inflammatory bowel disease (IBD)), gynecologic disorders(endometrial polyp, vaginal bleeding, endometriosis, dysfunctionaluterine bleeding, ovarian hyperstimulation syndrome, preeclempsia,polycystic ovarian syndrome (PCO), cervical cancer, and cervicaldysplasia), skin disorders (infantile hemangioma, verruca vulgaris,psoriasis, neurofibromatosis, epidermolysis bullosa, Stevens-Johnsonsyndrome, and toxic epidermal necrolysis (TEN)), eye disorders (maculardegeneration, maculopathies, diabetic retinopathy, and retinopathy ofprematurity (retrolental fibroplasia)) wound healing, inflammationassociated with immune responses, ischemia including limb ischemia andcardiac ischemia, Alzheimer's disease and other disorders such as wounddehiscence, Buerger Disease (thromboangitis obliterans, arteriosclerosisobliterans (ASO), ischemic ulcers) multiple sclerosis, idiopathicpulmonary fibrosis, HIV infections, plantar fasciosis, plantarfasciitis, Von Hippel-Lindau Disease, CNS hemangioblastoma, retinalhemangioblastoma, thyroiditis, benign prostatic hypertrophy,glomerulonephritis, ectopic bone formation, and keloids.

These different diseases are characterized by different changes invasculature structure. Accordingly, in one aspect of the invention,parameters and scoring methodologies are used to detect, diagnose, andmonitor particular diseases and their related therapies based uponparticular characteristics of vasculature structure indicative of thedisease. Even within each disease category, different diseases can becharacterized by different changes in vasculature structure.Accordingly, structure mining and scoring can be fine-tuned to increasethe sensitivity for particular types of disease within a category (e.g.,lung cancer score, breast cancer score, etc., can be developed).Patient-specific scoring parameters can also be developed to follow theprogression of a specific disease or disorder in a patient.

Structural vasculature changes include changes in vascular architectureand vascular morphology affecting blood vessels and/or lymph vessels.Structural changes can involve neovascularization (including the growthof large blood vessels (e.g., arteriogenesis) and the growth ofmicrovasculature (angiogenesis)), large blood vessel expansion, andvascular necrosis. Angiogenesis involves the formation of new bloodvessels that sprout from preexisting blood vessels. Angiogenesis isdifferent from vasculogenesis, which is the de novo formation of vesselsthat occurs primarily during development. Vasculogenesis is rarelyassociated with a disease or disorder. However, aspects of the inventioncan be used to study the natural process of vasculogenesis to helpidentify and understand defects in de novo blood vessel formation.

Angiogenesis is often associated with tumor growth and is a usefulbiomarker for cancer. Angiogenesis also can be associated withconditions where new blood vessel growth occurs in response to a reducedoxygen supply or blood flow (whether due to thrombosis, embolism,atherosclerosis, or other chronic occlusion or narrowing of thevasculature). Certain respiratory, cardiovascular, and inflammatorydisorders also are associated with angiogenesis.

Angiogenic blood vessels have structural characteristics that aredifferent from those of established blood vessels. For example, thebranching patterns and tortuosity of angiogenic blood vessels are verydifferent from those of normal blood vessels. These and other structuralfeatures are found predominantly in microvasculature and can be used formining and scoring vasculature structural images. However, changes inlarger blood vessels such as arteries and veins also may be associatedwith certain diseases or disease stages (e.g., growth and development oflarge tumors or late-stage tumors).

The vasculature that supports a tumor is typically associated with theconnective tissue of the tumor (the stroma) that supports the malignantcells (in the parenchyma). As discussed herein, tumor blood vessels areirregularly spaced and characterized by heterogeneous structuralpatterns or features. However, the formation of tumor blood vessels andother forms of angiogenesis may involve a series of characteristicstages (see, for example, Dvorak, 2003, American Journal of Pathology,Vol. 162:6, pp. 1747-1757, the disclosure of which is incorporatedherein by reference in its entirety). Early stage angiogenesis may becharacterized by vascular hyper-permeability, fibrin deposition and gelformation, and edema. This may result in the enlargement ofmicro-vessels such as venules. The cross-sectional area of an enlargedmicro-vessel may be about 4 fold that of a normal micro-vessel. Theperimeter of an enlarged micro-vessel may be about 2 fold that of anormal micro-vessel. Enlarged micro-vessels may occupy about 4-7 foldthe volume of normal micro-vessels in a region of active angiogenesis.The appearance of enlarged micro-vessels may be followed by theappearance of “mother” vessels that are enlarged, thin-walled,serpentine, and hyper-permeable. Mother vessels may undergo a process ofbridging whereby trans-luminal bridges are formed dividing the bloodflow within the vessel into smaller channels. A developing mother vesselalso may contain one or more glomerular bodies that may expand to dividethe lumen of the mother vessel into several smaller channels that aretypically tortuous. Bridging and glomerular body formation in mothervessels may lead to the appearance of small capillaries characteristicof angiogenesis. However, certain mother vessels persist as abnormallyenlarged vessels with thin walls. These vascular malformations are oftencharacterized by the presence of an asymmetric muscular coat andperivascular fibrosis. Small arteries and arterioles also may increasein size in diseased tissue. Aspects of the invention include detectingand/or monitoring any one or more of the blood vessel structural changesdescribed herein. In one embodiment, the presence of one or morepatterns (e.g., individual structural features or distributions)characteristic of new blood vessel formation may be used to detect ormonitor a disease. In another embodiment, the presence of one or morespecific patterns (e.g., individual structural features ordistributions) may be used to determine the stage of angiogenesis (e.g.,early-stage, mid-stage, late-stage, etc.) in a body region.

Accordingly, abnormal changes in blood vessel size (diameter and/orlength) can be early signs of diseases such as cancer or other diseaseassociated with an increased blood supply. Changes in blood vessel sizemay occur before any structural signs of angiogenesis appear. In oneembodiment, aspects of the invention are useful to detect blood vessels(e.g., capillaries) that are swollen and/or longer than normal. Forexample, aspects of the invention are useful to detect abnormally longintrapapillary capillary loops in situ (e.g., associated with earlystages of cancer in oesophageal mucosa).

In some embodiments, blood vessel changes indicative of necrosis intumor tissues may be indicative of the aggressiveness of the tumortissue and/or the likelihood of metastasis, and/or the responsiveness totherapy, and/or the efficacy of a therapeutic treatment (e.g., acandidate drug), and/or an therapeutic treatment selection and/ormodification (e.g., a change in drug or dose for an individual patient).Accordingly, in situ patterns (e.g., individual structural features ordistributions) indicative of necrosis may be useful biomarkers forpatient prognosis. In certain embodiments, necrosis within a region of atumor may be indicated by one or more of the following patterns (e.g.,individual structural features or distributions) within that region: acollapse in blood vessel structure, poor vascularization (e.g., a lowblood vessel density relative to other regions of the tumor or relativeto the perimeter of the tumor), a change in blood vessel size or shapeover time, a lower than threshold number of blood vessels, blood vessels(e.g., in the microvasculature or the capillaries) that are separated bya greater than threshold dikance (e.g., by more than 100 microns, morethan 150 microns, or more than 200 microns) within a volume of thetumor, micro-vessel diameter and/or density indicative ofundervascularization, etc., or any combination thereof In someembodiments, a volume of avascularization or undervascularization may beevaluated or quantified and used as an indicator of necrosis. It shouldbe appreciated that other indicia of necrosis may be used, alone or incombination with blood vessel features. Other indicia may includeindicia of tissue collapse or cavitation that may be visualized (e.g.,using CT etc.) and/or indicia of tissue viability using one or moremarkers of metabolic activity (e.g., ones that may be analyzed using aPET scan, etc.). One or more reference indicia (e.g., a reference volumeof avascularization or undervascularization may be identified byanalyzing vascular casts of necrotic tumor tissue (e.g., in a xenografttumor model, for example in an orthotopic or an ectopic tumorxenograft).

Aspects of the invention may be used for the detection (e.g., theautomatic detection)

Aspects of the invention may be used for the detection (e.g., theautomatic detection) of necrotic areas in a subject (e.g., in a tumor ina subject). A necrotic region is an avascular region within the boundaryof a diseased tissue. Methods of the invention may be used to detect(e.g., automatically) the transition between the vascularized diseasedtissue and avascular region that defines the boundary of the necroticregion.

Aspects of the invention also may be used to detect or evaluate (e.g.,automatically) a response to therapy. For example, a response to therapy(e.g., to a specific drug and/or a specific dosage of a drug, and/or toa combination of drugs and specific dosages of these drugs, etc.) can bedetected and assessed as follows. Changes in the vascular patterns (e.g.vessel normalization/straightening, disappearance of smaller diametervessels leading to lower micro-vessel density and to skewing of thevessel diameter distribution towards the larger vessels) may be detectedand/or evaluated within the volume defined by the boundary of thediseased tissue and the boundary of the necrotic area. An increase inthe absolute volume size of the necrotic area and/or the rate of suchchange while the total volume of the disease (e.g. tumor) volume staysconstant may be detected and/or evaluated as an indicator that thetherapy is effective. An increase in the ratio between the absolutevolume size of the necrotic area and the total disease (e.g., tumor)volume and/or the rate of change in this ratio may be detected and/orevaluated and used as an indicator that the therapy is effective. Aratio of the diseased tissue volume and the necrotic region volume maybe detected and/or evaluated and when it approaches 1 and the overalldiseased tissue volume starts shrinking it provides an indication that atherapy is effective. In some embodiments, reference indicia may beobtained from analyzing casts (e.g., appropriate vascular casts).However, reference indicia may be obtained from any suitable datarelating to blood vessel structures (e.g., view data, scan data, in vivodata, etc., or any combination thereof).

Structural representations of blood vessels can be mined to identify andevaluate certain patterns (e.g., individual structural features ordistributions) that can be used to provide a score that is related tothe probability that the blood vessels are normal or abnormal (e.g.,disease associated). Accordingly, in some embodiments a binned analysismay be predictive of a response to therapy.

In certain embodiments, a binned analysis may be sensitive tovasculature changes resulting from unwanted side-effects associated withone or more therapeutic drugs. Accordingly, binned analysis may be usedto detect or quantify toxic side-effects of certain drugs.

The morphology of blood vessels (e.g., binned blood vessels) can bemined to identify and evaluate certain patterns (e.g., individualstructural features or distributions) that can be used to provide ascore that is related to the probability that the blood vessels arenormal or abnormal (e.g., disease associated). Patterns (e.g.,individual structural features or distributions) for scoring bloodvessels include, but are not limited to, the following: diameter,curvature, tortuosity (including, for example, the degree of tortuosity,the length of the blood vessel along which abnormal tortuosity isobserved, etc.), variability or heterogeneity (including spatialvariability or heterogeneity over distance or in a volume), branchingshape or pattern, branching density, branching hierarchy, blood vesseldensity, distribution of vessel size (ratio of microvasculature tomacrovasculature) a field effect (the presence of blood vessels bendingtowards a specific region), blood vessel diameter distribution,variability of the geometric orientation of blood vessels or fragmentsthereof, and the distribution of the orientation(s) within a field. Thescore may have more significance if two or more (e.g., 3, 4, 5, 6, 7, 8,9, 10, or more, or all) of these parameters are evaluated. In someembodiments, a score is generated using one or more of these structuralparameters combined with additional information such as patient-specificmedical information (e.g., age, weight, height, gender, etc.) and thepresence of one or more additional indicators of disease such as avisible lesion on an X-ray or other image. In some embodiments, a scorecan be provided for a tumor. An example of a useful score is one thatreflects the vascularity of a tumor. An abnormally high vascularity(measured as a higher than normal blood vessel number, density, length,or combination of the above) is generally indicative of a moreaggressive or invasive tumor. In one embodiment, vascularity isevaluated by measuring the volume of the lumen of angiogenic vasculature(the volume within the blood vessel tree associated with a tumor). Inanother embodiment, a measure of vascularity is provided by dividing thevolume of the angiogenic lumen by the volume of the solid tumor.Additional information can be gleaned from obtaining a score (or otherstructural evaluation) at two or more times. A changing score (or otherstructural evaluation) is indicative of an evolving vasculature thatcould be associated with a disease or disorder. It should be appreciatedthat the patterns (e.g., individual structural features ordistributions) described herein can be identified and analyzed for afield of analysis without imposing a connectivity on the vessels beingstudied. In some embodiments, it may be sufficient to analyze onlyfragments of blood vessels in order to detect one or more structuralfeatures of individual vessels or geometrical features of a field ofvessels that are different from normal features. For example, bloodvessel fragments having an average length of 0.5 mm, 1 mm, 5 mm, 10 mm,50 mm, 1 cm, 5 cm, 10 cm, 50 cm, etc. may be used. However, it should beappreciated that shorter or longer or intermediate lengths may be used.The scoring and mining aspects of the invention described herein can beautomated. Accordingly, diseased (e.g., angiogenic) vasculature can beautomatically detected amidst normal vasculature. Various vasculatureparameters can be automatically detected and scored, either separatelyor in any combination, including vessel tortuosity, vessel branching,vessel density, and total intra-vascular volume, but the invention isnot limited to any particular parameter or combination.

In one embodiment, aspects of the invention can be used to detectblocked blood vessels, and thromboembolic events, including stroke, lungemboli, blocked micro-coronaries, deep-vein thrombosis, etc. Blockedblood vessels can be detected (1) directly by detecting structuralchanges in the blocked blood vessel (e.g., detecting a clot, wallthickening, or other signs of reduced flow) and/or (2) indirectly bydetecting new vasculature that was generated in response to theblockage. In general, the formation of collateral blood vessels is moreordered than angiogenesis associated with cancer. One to aspect of theinvention described herein also allows clots to be detected in smallblood vessels.

As discussed herein, aspects of the invention can be used to screen theentire vasculature structure of a human or other animal to screen forany form of abnormality in any tissue. Alternatively, a subset of thebody may be screened. Accordingly, the structures of binned vessels canbe analyzed for one or more organs or tissue types. In addition, only aportion of the vessels in any predetermined bin may be analyzed withinany target volume as opposed to the entire vascular tree in that volume.This may be done by analyzing structure data focused on the area ofinterest, or large amounts of structure data may be obtained, but ananalysis may be restricted to a subset of the available data. In someembodiments, only a portion of a vascular tree may be binned and/oranalyzed, for example only a portion of those vessels that are of aparticular size range. In some embodiments, only fragments of a vasculartree are represented and/or analyzed if the fragments are sufficientlyinformative to provide patterns (e.g., individual structural features ordistributions) of interest. Fragments may include branches or may beunbranched. The portion of the vasculature being analyzed may bestatistically significant, such that any observation (normal orabnormal) is physiologically significant. For example, branchedstructures may not be required for the analysis if a sufficient numberof vessel substructures are analyzed to confidently detect any otherpatterns (e.g., individual structural features or distributions) thatmay be associated with vasculature changes (e.g., angiogenesis) such ashigh vessel density. In aspects of the invention, vascular patterns maybe detected and/or evaluated in situ in a volume of 1 mm³, 2 mm³, 5 mm³,1 cm³, 2 cm³, 5 cm³, 10 cm³, etc. However, smaller or larger orintermediate volumes also may be analyzed. In some embodiments, vascularpatterns or structures are evaluated over an entire model tissue ororgan (e.g., for an entire orthotopic or ectopic tumor model).

Different tissues and organs have different and characteristic bloodvessel patterns (e.g., the lung which is highly vascularized).Accordingly, in one embodiment, structural analyses and associatedstructural parameters may be optimized for evaluating different tissues.

In some embodiments, scan data is obtained and/or analyzed for one ormore organs (e.g., lung, heart, colon, brain, liver, pancreas, kidney,breast, prostate, etc.) or tissue (e.g., skin, bone, etc.) or portion ofany of the above.

Brains may be evaluated for signs of brain tumors and/or otherneurological disorders that can be associated with changes in vascularpatterns. For example, Alzheimer's may be associated with certainvascular abnormalities. In one embodiment, one or more changes in bloodvessel pattern (e.g., shape and/or size) may be detected as an indicatorof high blood pressure in the brain.

In some embodiments, certain specific regions of organs or tissues arefocused on. For example, atherosclerosis is typically found in certainparts of the arterial tree (e.g., bifurcations, side branches, regionsopposite flow dividers, and other areas where angiogenesis often occursin association with atherosclerosis) and certain cancers tend to occurmore frequently in certain organ or tissue regions (e.g., colon cancersare not distributed evenly along the length of the colon).

In other embodiments, aspects of the present invention may be used tofollow up with individuals who have been identified as having one ormore other indicia of disease (e.g., fecal occult blood, a colon polyp,a lung nodule, one or more cysts or other indicia of disease). Aspectsof the invention may be used to confirm the presence of a disease,determine a location for the disease-associated lesion, or provide anevaluation or prognosis of a disease. For example, aspects of theinvention may be used to determine whether abnormal vasculature ispresent at the site of a lesion (e.g. a colon polyp, a lung nodule, abladder cyst, a prostate cyst, a breast cyst, a spot on a mammography,or any other cyst, lump, or spot that may be detected physically,visually, or using any other diagnostic technique) and help evaluate thelikelihood of a malignancy (or other carcinogenic disease stage)associated with the lesion. Accordingly, aspects of the invention may beused for virtual malignancy detection (e.g., virtual colonoscopy,virtual colon malignancy detection, virtual bronchoscopy, virtual lungmalignancy detection, virtual mammography, virtual cystoscopy, etc.).

In other embodiments, aspects of the invention may be used for screeninga cancer patient to evaluate the extent of a cancerous lesion and/or toscreen for the presence of one or more metastatic lesions (e.g., one ormore loci associated with angiogenesis). A cancer patient may bescreened upon initial diagnosis of a primary cancer. In addition oralternatively, a cancer patient may be screened at least once after aninitial cancer treatment (e.g., surgery, radiation, and/orchemotherapy). This screening may include the original cancer locus todetect any cancer recurrence. This screening may include similar bodytissue to screen for the presence of other lesions in the same tissue ororgan (e.g., the entire colon may be screened when a cancerous lesion isdetected in one region of the colon, the second breast may be screenedwhen a cancerous lesion is detected in one breast, etc.). This screeningalso may be extended to the whole body or to one or more other locisuspected of containing a metastatic lesion. In one embodiment, a cancerpatient may be screened several times after an initial cancer treatment(e.g., at time intervals of about 6 months, about 1 year, about 2 years,about 5 years, or at other time intervals).

In one embodiment, a follow up procedure may involve screening one ormore organs or tissues for the presence of a metastatic lesion.Different cancers may have different characteristic patterns ofmetastasis. Accordingly, different target loci may be screened fordifferent cancers. For example, metastatic breast cancer typicallyspreads to the lungs, the liver, bone, and/or the CNS. Therefore, one ormore of these tissue types or organs may be screened after a patient isdiagnosed with breast cancer. Similarly, other target loci may bescreened after a patient is diagnosed with another cancer type. In someembodiments, the entire body of a cancer patient may be screened forindicia of metastasis.

In one aspect, an initial screen may be performed on an entire body, oran entire organ, using a low resolution representation and/or, forexample, analyzing only one or two or a small number (e.g., less thanfive) pattern parameters in order to detect indicia of a disease.Subsequently, the presence and or nature of the disease may be diagnosedusing a higher resolution representation and/or, for example, analyzingone or more additional pattern parameters or alternative patternparameters than those that were analyzed for the initial detection.

In some embodiments, small changes in blood vessel distributions may beobserved (for example as measured by a ratio between the number of bloodvessels of two or more different sizes in a region of interest, forexample, a tumor in an animal model) and used as a biomarker. Suchbiomarkers may represent early changes (e.g., early changes in tumorgrowth or response to therapy) that occur before later changes in tumorsize and/or tumor morphology. It should be appreciated that some or allof the diagnostic aspects of the invention can be automated as describedherein.

It should be appreciated that some or all of the diagnostic aspects ofthe invention can be automated as described herein.

Aspects of the invention also can be used to identify the location of adisease by locating one or more structural abnormalities associated withthe disease. This information can be used to target a biopsy procedureor a treatment (e.g., a treatment with one or more toxic chemicals,radiation, heat, cold, small molecules, gene therapy, surgery, any othertreatment, or a combination of two or more of the above) to the preciselocation of a disease lesion, or for any other purpose.

In one embodiment, an imaging device is connected to a computer thatprovides a real-time visual display of the disease lesion. In oneembodiment, a real-time visual display may be an accurate model of abody region and lesion along with associated vasculature (as opposed toan actual image). This visual information can be used to guide asurgical instrument for a biopsy. Alternatively, the information can beused to guide an invasive (e.g., surgical removal or bypass) ornon-invasive (e.g., radiation) treatment procedure to the site of thedisease lesion (e.g., tumor or blood clot).

In some embodiments, aspects of the invention may be used to define theboundary between diseased and non-diseased tissues, or between necroticand non-necrotic tissue, etc., or any combination thereof. For example,a boundary may be identified or defined by analyzing binned data forseveral areas of interest and identifying adjacent areas having verydifferent blood vessel densities (or differences in other morphologicalparameters that are associated with disease, necrosis, etc., or anycombination thereof.

In one embodiment, aspects of the invention may be used to identify anarea of tissue for treatment before the treatment is applied. Forexample, a treatment target region may be identified by detecting aboundary of chaotic blood vessel structures. The area may be assessedafter treatment to confirm that the treatment was appropriatelytargeted. In one embodiment, a structure may be analyzed pre-operativelyto identify the extent of tissue to be removed from a body region. Inone embodiment, a body region may be analyzed post-operatively todetermine whether any abnormal structures were missed. This may be usedto confirm the success of a radiation treatment or a surgical removal ofdiseased tissue. Alternatively, this may be used to decide on furthersurgery and/or another form of treatment. In another embodiment, adisease boundary may be defined or depicted by the boundary of abnormalvasculature. A treatment (e.g., radiation therapy, surgery, etc.) may beguided by and/or restricted to a volume encompassed by the diseaseboundary.

In one embodiment, aspects of the invention can be used to evaluate thesuccess of a surgical implant or transplant. For example, aspects of theinvention can be used to evaluate the formation of new blood vesselsafter an organ or tissue transplant.

In another embodiment, the development of new blood vessels may bemonitored after removal of tumor tissue or after a tumor biopsy, both ofwhich may trigger angiogenesis and/or convert a dormant tumor into amalignant tumor.

It should be appreciated that some or all of the interventional aspectsof the invention can be automated as described herein.

Aspects of the invention also can be used to optimize a therapeutictreatment for a patient. The extent of disease progression or regressioncan be monitored in response to different treatment types or dosages,and an optimal treatment can be identified. The optimal treatment maychange as the disease progresses. The effectiveness of the treatmentover time can be monitored by analyzing changes in disease-associatedpatterns (e.g., individual structural features or distributions) usingthe aspects of the present invention described herein.

In one embodiment, a first therapy can be administered and itseffectiveness on slowing, stopping, or reversing abnormal blood vesselgrowth can be monitored either irregularly or at certain time intervals(e.g., daily, weekly, monthly, or other time intervals). In someembodiments, if a first therapeutic regimen does not have a desiredeffect on disease progression, a second therapeutic regimen can beevaluated. Similarly, additional therapeutic regimens can be evaluatedon a patient-by-patient basis. Additionally, the invention can be usedto optimize a chosen therapeutic regimen (e.g., optimize dosage, timing,delivery, or other characteristic of a drug or other treatment) bymonitoring the effect of minor therapeutic changes and using theconditions that appear to be most effective for the condition and thepatient.

When looking at the therapeutic effectiveness of a treatment,disease-specific parameters may be monitored. Of course, all parameterscan be obtained and only a subset reviewed. However, it may be moreefficient to simply obtain binned data only for those parameters thatcharacterize the disease.

According to aspects of the invention, patterns (e.g., individualstructural features or distributions) that are used to detect angiogenicvasculature and other abnormal blood vessels also can be used to monitora disease response to treatment. For example, the total vascularity orany other volumetric analysis of angiogenic or other diseasedvasculature, and the distribution of vessel size (e.g., a ratio of smallto large blood vessels) can be used independently or together asindicators of disease progression or regression. In general,microvasculature disappears before macrovasculature if ananti-angiogenic treatment (or other disease treatment) is effective.Therefore, an effective treatment results in a shift in the distributionof blood vessel sizes towards larger vessels. An index ofanti-angiogenic activity can be scored as either a loss of small bloodvessels or a shift of observed blood vessels towards a single size (orboth).

In another aspect, the parameters can be (or include) changes over time.For example, a structure present at a second time can be compared to astructure present at a first time. In one embodiment, a disease may betracked pre-therapy and/or post-therapy. Naturally, additional timepoints can be used. The time points may depend on the condition beingobserved (e.g., is it the progression of a disease that is alreadyidentified, is it the screening of patient(s) over time). Time periodscan be daily, weekly, monthly, annual, or shorter, intermediate orlonger time periods. Time intervals may be a series of regular timeperiods. However, other time intervals may also be useful. In oneembodiment, a patient-specific baseline is established and monitoredover time. For example, vasculature changes in the colon, breast, orother tissue or organ can be monitored periodically.

In one aspect of the invention, a type of treatment may be determined bythe degree or extent of abnormal vascular structures (e.g.,angiogenesis) that is detected at one or more suspected disease loci(e.g., cancerous loci). For example, if a suspected cancerous locus ormetastasis is pre-angiogenic or associated with early stageangiogenesis, it may be appropriate to monitor the locus without anyform of treatment. However, an appropriate therapy may involve theadministration of one or more angiogenesis inhibitors to prevent theformation of any new vasculature. If a suspected cancerous locus ormetastasis is associated with mid-stage angiogenesis, an appropriatetherapy may be the administration of one or more angiogenesisinhibitors. A patient with mid-stage angiogenesis at a suspected locusalso should be monitored so that any further blood vessel developmentcan be treated more aggressively. If a suspected cancerous locus ormetastasis is associated with late stage angiogenesis, an appropriatetreatment may involve at least one or more of chemotherapy (e.g.,cytotoxic chemotherapy and/or hormone-based chemotherapy), radiation,surgery, and/or treatment with one or more angiogenesis inhibitors.However, it should be appreciated that any of the above treatmentoptions may be used to treat a patient with any one or more lesionsassociated with any degree of angiogenesis.

Examples of angiogenesis inhibitors include but are not limited to2-methoxyestradiol (2-ME), AG3340, Angiostatin, Angiozyme, AntithrombinIII, VEGF inhibitors (e.g., Anti-VEGF antibody), Batimastat, bevacizumab(avastatin), BMS-275291, CAI, 2C3, HuMV833 Canstatin, Captopril,Cartilage Derived Inhibitor (CDI), CC-5013, Celecoxib (CELEBREX®),COL-3, Combretastatin, Combretastatin A4 Phosphate, Dalteparin(FRAGIN®), EMD 121974 (Cilengitide), Endostatin, Erlotinib (TARCEVA®),gefitinib (Iressa), Genistein, Halofuginone Hydrobromide (TEMPOSTATIN™),Id1, Id3, IM862, imatinib mesylate, IMC-IC11 Inducible protein 10,Interferon-alpha, Interleukin 12, Lavendustin A, LY317615 or AE-941(NEOVASTAT™), Marimastat, Maspin, Medroxpregesterone Acetate, Meth-1,Meth-2, Neovastat, Osteopontin cleaved product, PEX, Pigment epitheliumgrowth factor (PEGF), Platelet factor 4, Prolactin fragment,Proliferin-related protein (PRP), PTK787/ZK 222584, ZD6474, Recombinanthuman platelet factor 4 (rPF4), Restin, Squalamine, SU5416, SU6668,SU11248 Suramin, Taxol, Tecogalan, Thalidomide, Thrombospondin, TNP-470,TroponinI, Vasostatin, VEG1, VEGF-Trap, and ZD6474.

Some embodiments may include a method of selecting a subject fortreatment and/or selecting a treatment or a course of therapy based onthe analysis of certain in situ vascular structures. A method mayinvolve analyzing in situ vascular structure(s) in a human subject toobtain, for example, a score. The score may be compared to a controlscore (e.g., in an apparently healthy population) or to a previous scorefrom a previous analysis on the same subject. The treatment or thecourse of therapy may be based on such a comparison. In someembodiments, obtaining an analysis of vascular structures is repeated soas to monitor the human subject's response to therapy over time. In someembodiments of this aspect of the invention, the method furthercomprises measuring a second index of disease in the human subjectwherein deciding on the treatment or course of therapy is also basedupon the measurement of said second index.

In certain embodiments, patients having a tumor that isunder-vascularized (e.g., one that shows signs of necrosis) may beselected for treatment with one or more anti-angiogenic compounds.Under-vascularized tumors may be identified as those that have a lowdensity of blood vessels, or for which the blood vessel diameters arelow (e.g., below a threshold number typical of vascularized tumors).

Aspects of the invention also may include monitoring the effectivenessof a therapy by monitoring the presence of blood vessel patterns orfeatures over time. For example, the progressive loss of blood vesselsin a tumor in response to treatment may be a sign that a therapy iseffective. In contrast, the absence of any impact on vascularization maybe an indicator that a treatment is not being effective in a patient andthat an alternative therapy should be considered or used.

It should be appreciated that some or all of the therapeutic aspects ofthe invention can be automated as described herein.

In one embodiment, aspects of the invention can be used to understandstructural changes associated with biological processes of interest(e.g., disease development and progression). For example, an animal'svasculature can be analyzed to identify additional patterns (e.g.,individual structural features or distributions or changes associatedonly with certain binned size ranges) that may be associated with woundhealing or different diseases or different disease stages. Theseadditional patterns (e.g., individual structural features ordistributions) may be used in one of more of the diagnostic,intervention, therapeutic, and development aspects of the invention.

In one embodiment, aspects of the invention can be used to understandstructural changes associated with medical procedures. For example, ananimal's vasculature can be analyzed to identify changes associated withpost-surgical wound healing or implant/transplant (including xenografts)growth or rejection.

It should be appreciated that some or all of the research aspects of theinvention can be automated as described herein.

In another embodiment, aspects of the invention can be used in screensof compound libraries or to validate candidate compounds for treatingdiseases associated with abnormal internal structures (e.g., abnormaltubular networks). Aspects of the invention allow efficient highthroughput analyses of internal structural changes using binned data(e.g., BMVD). These changes can act as surrogate markers (biomarkers)for certain diseases. As a result, the screening process can beautomated to a large extent, and the time for obtaining resultssignificantly shortened when compared to current validations that ofteninvolve waiting for disease symptoms to change and also may requiretissue biopsies.

Aspects of the invention may be used for identifying and quantifyingvascular patterns (e.g., structural features) that can be used assurrogate markers for diagnostic, therapeutic, and research anddevelopment purposes. Surrogate markers are useful for reducing the timeof diagnosis, therapy evaluation, and drug development. A surrogatemarker can be used as an early indicator for disease diagnosis, diseaseprognosis, or drug effectiveness, without waiting for a clinical outcome(e.g., increased survival time in response to a drug). So, a vasculatureanalysis can be used as a surrogate marker for drug development (in bothpre-clinical and clinical trials), for clinical screening (e.g., breast,lung, or colon screening), and for clinical therapy monitoring. Forexample, binned vasculature structure may be a useful surrogate markerfor angiogenesis related diseases such as cancer.

In one embodiment, aspects of the invention provide methods forscreening and/or validating candidate compounds or therapies for theireffectiveness in treating neo-vasculature formation and/or vasculaturepattern changes associated with disease. Aspects of the invention may beused to evaluate individual or small numbers of compounds or to screenlibraries to evaluate and/or identify a plurality of candidate compounds(e.g., by administering these compounds, individually or in groups, toan experimental animal such as a mouse and evaluating their effect onangiogenic vasculature). Libraries may contain any number of compounds(e.g., from approximately 100 to approximately 1,000,000) Differenttypes of compounds can be screened, including antibodies, smallmolecules, etc., or any combination thereof. However, the invention isnot limited by the number and/or type of compounds that can beevaluated.

In one embodiment, the effectiveness of a candidate compound can becompared to a reference compound. A reference compound can be anycompound with a known effect on a structure. For example, Avastin(Genentech) is a known monoclonal antibody against vascular endothelialgrowth factor (VEGF) that can be used as a reference to test the effectof a candidate compound on neovasculature growth. Other examples ofcompounds include, but are not limited to, Sutent and Nexavar.

It should be appreciated that some or all of the development aspects ofthe invention can be automated as described herein.

It also should be appreciated that any one or more geometrical,structural, and/or distributional parameters described herein may beevaluated by comparison to a reference parameter. In some embodiments, areference parameter may be an amount or score for that parameter in anormal or healthy subject. In other embodiments, a reference mayrepresent a diseased condition. In some embodiments, a change or amountof any structural parameter that is correlated or associated with adisease or condition as described herein may be a statisticallysignificant change or difference in that parameter in a diseased or testsubject relative to a reference subject. In some embodiments, adifference or change in a structural parameter may be an increase or adecrease in a particular parameter (or a combination of parameters). Anincrease in a parameter may be at least a 5%, 10%, 20%, 30%, 40%, 50%,60%, 70%, 80%, 90%, 100%, or greater increase in that parameter in atest subject relative to a reference subject. Similarly, a decrease inthat parameter may be at least a 1%, 5%, 10%, 20%, 30%, 40%, 50%, 60%,70%, 80%, 90%, 100%, or greater decrease of a measure of that parameterin a test subject relative to a reference subject. Once an amount ofchange or difference in a parameter has been correlated or associatedwith a disease or condition, that level may be used in subsequentmethods according to the invention. Accordingly, in some embodiments, adifference of at least at least 1%, 5%, 10%, 20%, 30%, 40%, 50%, 60%,70%, 80%, 90%, 100%, or more of any given structural parameter (e.g.,tortuosity, density, volume, or any other individual structural featureor distribution of structures or structural features as describedherein) within a data bin relative to a reference value may be used as athreshold for methods of the invention. It should be appreciated thathigher or lower or intermediate values may be used. It also should beappreciated that different parameters may have different threshold orreference levels. Also, different parameters (and/or different levelsfor each parameter) may be associated with different conditions ordiseases. Accordingly, specific disease or condition values orthresholds may be identified for different parameters or combinationsthereof. These threshold values may be used for disease detection,diagnosis, monitoring, or for any other therapeutic, clinical, orresearch application described herein (e.g., in automated methodsdescribed herein).

Accordingly, aspects of the invention provide methods and devices forobtaining and/or analyzing data relating to internal tubular structuresin casts and/or in human and/or other animal bodies. In someembodiments, methods of the invention involve analyzing one or moreparameters (or parameter changes over time) for binned blood vesselsthat have been categorized based on their size. For example, bloodvessels may be binned according to the following non-limiting diameterranges: about 0-10 microns, about 10-25 microns, about 25-50 microns,about 50-75 microns, about 75-100 microns, about 100-150 microns, about150-200 microns, about 200-300 microns, about 300-400 microns, about400-500 microns, about 500-1,000 microns, or any combination thereof.However, any other suitable bin size ranges (including larger, smaller,or intermediate size ranges) may be used. In some embodiments, thenumber of different bins may be between about 2 and about 10. However,higher numbers of bins also may be used. In some embodiments, only 2 to5 bins are used (e.g., 2, 3, 4, or 5). In certain embodiments, threeblood vessel bin sizes are used: small, medium, and large. In someembodiments, a single bin is chosen having a predetermined size rangeand no other size ranges are analyzed.

Profiles may be extracted from the distribution of quantitative valuesfor one or more structural features as described herein (including forexample, features observed in vascular casts). In some embodiments,volume independent or density independent profiles may be extracted fromdistributions by comparing ranges within each distribution beinganalyzed (e.g., a subpopulation within a single range as a percentage ofthe total population across all ranges, or a ratio of subpopulationswithin a first and a second range that each represent different subsetsthe entire range of values).

Aspects of the invention may include the analysis of one or more regionsof interest in animal disease models (e.g., in situ and/or in casts ofone or more regions of interest). Animal disease models may be, but arenot limited to, engineered (e.g., recombinant) animals, transgenicanimals, metastatic cancer models, xenograft models, orthotopictransplant models, etc., or any combination thereof. In someembodiments, different animal models may have different known geneticmarkers (e.g., particular mutations) associated with a disease ofinterest (e.g., a cancer). Any suitable animal may be used as an animalmodel, including, but not limited to, a mouse, rat, hamster, guinea pig,pig, dog, cat, rabbit, zebrafish, or other suitable animal. It should beappreciated that whole experimental animals may be analyzed. However, insome embodiments, tissues and/or organs may be analyzed. In someembodiments, models may be based on xenografts (e.g., xenografts ofcancer or tumor cells that will form cancer or tumor tissues in a hostanimal). For example, human cells may be introduced into a non-humanhost animal. Other uses of xenografts include analyzing responses tocertain tissue and/or organ transplantation (e.g., a non-human tissue ororgan into a human host). In some embodiments, vascular casts of regionsof interest in an animal model may be obtained to thoroughly analyze thevascular structures, and/or changes therein, associated with thecondition being modeled. In some embodiments, observations made on castsmay be compared (e.g., using appropriate statistical techniques) to invivo (e.g., in situ) observations to identify one or more commonstructural characteristics and/or changes that are statisticallysignificant in vivo in association with a disease, condition, orresponse of interest. These can then be used in subsequent applicationsas described herein.

According to aspects of the invention, compounds and therapies can beevaluated in the context of an in-vivo model such as an animal diseasemodel. For example, a mouse with cancer or atherosclerosis can be usedto evaluate, optimize, and identify useful therapies. Other animalmodels also can be used. Aspects of the invention may be useful forhigh-throughput analyses because they can detect small changes invasculature and can be used to evaluate a therapy in a short time periodwith minimal manipulation since little or no invasive procedures arerequired.

Vascular analysis aspects of the invention can be used on an orthotopicmodel to test, for example, the effectiveness of a drug in a shortperiod of time. For example, the effect of a candidate drug onangiogenesis in an orthotopic mouse tumor model may be quantifiableafter about 5 days (e.g., between 1 and 10 days, depending on the modeland the drug). In contrast, a subcutaneous cancer animal model requiresapproximately one month for tumor growth to be analyzed and compared tocontrols.

An orthotopic model can be used to model different diseases or clinicalconditions. Examples include, cancer, tissue regeneration, wound healing(including healing after traumatic injury, healing after surgicalintervention, healing of burnt tissue such as skin), tissue or organtransplant therapy, medical device implant therapy, other conditionsassociated with neovascularization or changes in normal vascularstructure, or any combination of two or more of the above. However, theinvention is not limited by the type of orthotopic model or the type ofdisease or clinical condition that is being analyzed.

A single orthotopic disease model animal may be useful for testing morethan one candidate drug molecule since the analysis does not involvesacrificing the model animal. Accordingly, once a test with a firstcandidate is complete, a subsequent candidate can be evaluated in thesame model animal. A series of candidates can be tested in a singlemodel animal, with appropriate controls, provided the model retainsfeatures of neovascularization that are necessary for the assay.

It should be appreciated that any of the geometrical, structural, and/ordistributional parameters described herein may be used as biomarkers.Biomarkers of the invention can be qualified and/or quantified andcompared using standard statistical methods. These biomarkers can becompared on individual basis, but also in combination as a signature ofvascular morphology and function. Whole signatures can be comparedbetween treated and untreated samples, or samples with physiological andpathological vascular pattern.

It should be appreciated that in some embodiments, one or more of thebiomarkers described herein may be used to aid in the diagnosis,prognosis, prediction, or other medical application along with othertypes of physiological and or biological markers (e.g., physiologicalmeasurements, genetic markers, etc., or any combinations thereof).

It should be appreciated that aspects of the invention may be applied tofeatures of vascular geometry (e.g., curvature, tortuosity,distributions of vascular structural features, etc., or any combinationthereof) that are obtained from an analysis of vascular casts (e.g.,using any suitable image analysis technique described herein or known inthe art). In some aspects, vascular casts are analyzed to identifydistributions of one or more blood vessel structural features(including, for example, abnormal excess or absence of blood vessels orblood vessel structures) that are associated with a disease or othercondition of interest. Structural features identified in casts may beused as biomarkers or references to evaluate in situ vasculature, forexample, to detect indicia of a disease or other condition of interestin a subject. Structural characteristics of vascular casts also may beused to evaluate therapeutic treatments, screen candidate compounds, andfor other applications as described in more detail herein. In someembodiments, one or more structural parameters are analyzed over time(e.g., using a series of vascular casts obtained at different timepoints) to monitor and/or identify structural changes that occur duringdevelopment, disease progression or regression, or in response totherapy. In some embodiments, structural analysis is performed onvascular casts obtained from experimental models (e.g., whole animalmodels, or organ or tissue models). However, in some embodiments,vascular casts are obtained and analyzed for one or more regions ofinterest (e.g., diseased regions) in dead animals, including for exampledead humans (e.g., human cadavers).

As used herein, a vascular cast refers to a physical structure that isgenerated to represent blood vessels of an entire vasculature or portionthereof. A cast may be obtained by perfusing a vasculature or a vascularregion (e.g., the blood vessels of an organ, for example, of a kidney orliver) with a casting material that solidifies (e.g., polymerizes) toform a stable structure. The surrounding tissue and cells (e.g.,including the blood vessel walls) may be removed to reveal the cast. Thecast retains the structural features of the original blood vessels. Castmay include structures of blood vessels of different sizes as describedherein. Certain casts are more flexible than others, certain casts aremore brittle than others. Vascular casts can be used to identifyvascular structural features with high resolution and/or to identifycorrelations between structural features and conditions of interest withhigh degrees of confidence since the structures of the blood vessels areretained in the casts and other biological structures that couldinterfere with an analysis are removed. Vascular casts may be obtainedusing any suitable casting material. In some embodiments, the castingagent may be a polymer. In some embodiments, the casting agent may reactwith the blood vessel walls. Non-limiting examples of casting agentsinclude, but are not limited to Microfil®, methyl methacrylate,prepolymerized methyl methacrylate (Mercox™), Mercox™ CL-2B, otheracrylic resins, silicon, gold nanoparticles, Batson No. 17,polyurethane-based casting agents (e.g., PU4ii), etc., or combinationsof two or more thereof.

It should be appreciated that casting agents may be supplemented withcontrast agents and/or other detectable agents. Examples of contrastagents include, but are not limited to, BaSo₄ and UAc (e.g., mixed intothe casting material). In some embodiments, already polymerized castscan be soaked in OSO₄ to achieve better contrast using CT imaging. Incertain embodiments, any suitable heavy metal can be mixed into theresin to make it more radioopaque.

In some embodiments, a large volume of an animal body (e.g., the entirebody) may be perfused with a casting agent composition. In certainembodiments, a small volume of an animal (e.g., a tissue, an organ or aregion of either one thereof) may be perfused with a casting agentcomposition. In some embodiments, a casting agent may be perfused into atissue or an organ or a region of either one thereof after removal froman animal (e.g., after biopsy or other surgical excision). In someembodiments, a casting agent composition may be perfused into a liveanimal. It should be appreciated that an animal may be sacrificed afterperfusion with a casting agent depending, in part, on the amount andtype of casting agent composition that is used and the tissue or organto which the casting agent composition is targeted. According to aspectsof the invention, casting agent(s) may be used to preserve in vivostructures for detailed analysis. In some embodiments, this analysisidentifies particular structural or distribution properties that can besubsequently used as markers for in vivo diagnostic, therapeutic,research, and/or other applications in live animals (including humans).

In some aspects, vascular structures may be analyzed in situ in ananimal after perfusion with a casting agent composition. In someaspects, a tissue or an organ or a region of either one thereof may beremoved from an animal for analysis (e.g., before or after perfusionwith a casting agent composition).

Accordingly, aspects of the invention can be used to represent and/orvisualize blood vessels with a casting agent or medium.

Data relating to one or more selected structures (e.g., structuralpatterns obtained from an analysis of a vascular cast) may be obtainedand/or analyzed to glean information about a physiological condition ofan animal based on the structure (or changes in the structure). Forexample, patterns identified in casts may be used as biomarkers toscreen in situ vasculatures for the presence of one or more similarpatterns or to quantify the extent of the pattern in situ. Thisinformation may be used for diagnostic, predictive, prognostic,therapeutic, interventional, research and/or development purposes, aswell as for grading and/or staging a disease. In some embodiments,methods of the invention may involve analyzing one or more structuralparameters (or one or more structural parameter changes over time) basedon binned structure data or information obtained for casts (e.g.,vascular casts) or in situ structures (e.g., in vivo blood vessels).

In some embodiments, one or more structures and/or structural changesthat are identified using casts may be detected or monitored in vivo todetermine whether a predetermined disease, condition, or response ispresent in vivo.

In some embodiments, structural parameters and/or structural changesobserved for vascular casts from experimental animals (or organs ortissues) can be used as references when analyzing vasculature in vivo.For example, structural vasculature parameters and/or changes that areidentified in casts using experimental animal models subsequently can bedetected or monitored in vivo (e.g., in a human subject) and used toevaluate the development of a disease, a drug response or otherbiological or disease property associated with the vasculatureparameters and/or changes in a subject. In some embodiments, structuralcharacteristics identified in vascular casts may be used to identify oneor more patient subpopulations that are (or are predicted to be) moreresponsive to a particular treatment. For example, responsive subjectsmay be identified as those having one or more blood vesselcharacteristics that were associated with responsiveness in animalmodels and identified by analyzing vascular casts from the responsiveanimals.

One or more of the characteristics described herein, or combinations ofcharacteristics, or related structural changes over time, may beidentified as structural patterns that can be associated with one ormore conditions of interest. Once identified, these patterns can be usedas biomarkers to identify or monitor the conditions of interest in vivoin a subject, for example, by analyzing the in situ vasculature of thesubject (or a portion thereof) and detecting the presence of and/orquantifying the extent of a specific vascular structural pattern.

Accordingly, one or more of the following non-limiting structuralcharacteristics (e.g., combinations of 2, 3, 4, 5, 6, 7, 8, 9, 10 or allof the following structural characteristics) may be evaluated (e.g.,quantified) in vascular casts and/or in situ (e.g., in vivo): diameterbinned vessel distribution, mean vessel diameter distribution, branchingpoint density, vessel branching distribution, angle of vessel branchingdistribution, interbranching distances, vessel density, vesseltortuosity, intervessel distances, luminal vessel surface, vesseldilation (changes in vessel diameter over a segment), sinosoidalation(dilation in sinosoids), or permeability (vessel leakiness).Distributions of the quantified characteristics may be prepared andanalyzed (e.g., compared). However, it should be appreciated that otherstructural characteristics, for example, other characteristics describedherein also may be analyzed by analyzing and comparing distributions ofthose characteristics or features.

For example, the quantification of any of the following non-limitingfeatures may be performed and related distributions may be analyzed asdescribed herein: Total Intra-Vascular Volume (TIVV)—e.g., over theentire Tumor Vascular Tree and Region of Interest (ROI), over only theSmall Vessels Volume within the Total Volume (or the ROI), over only theMedium Vessels Volume within the Total Volume (or the ROI), or over onlyLarge Vessels Volume within Total Volume (or the ROI); Intra-VascularVolume Distribution (IVVD)—e.g., broken by Total Volume, Small, Mid &Large Vessels Volumes, color encoded into small, mid, large vessels on asegmented vascular tree (e.g., based on a Poker Chip representation),linked vascular volume values through color encoding of regions within asegmented vascular tree (e.g., on a Poker Chip representation), ordetected locations/regions of Max Volume, Mid Volume, Min Volume andlink to regions within a segmented vascular tree (e.g., based on a PokerChip representation); Inter-Vessel Distance (IVD)—e.g., in the form ofaverage/Min/Max values, histograms, values in select locations (forexample single locations), color encoded Vessel Tree/ROI(s) with IVDvalues & IVD Value Clusters; Inter-Branching Distance (IBD)—e.g., in theform of average/Min/Max values, histograms, values in select locations(for example single locations), color encoded Vessel Tree/ROI(s) withIBD values and IBD Value Clusters; Vascular Diameter Variability (VDV)along the length of the vessel—e.g., in the form of histograms for theentire vascular tree or w/in a ROI, with the ability to view suchvariability for a single vessel or a group of vessels on the whole treeof within select (ROI)s, or color encoded segments within a tree/ROI(e.g., based on a Poker Chip representation) based on VDV values; VesselBranch Curvature (VBC) and Tortuosity (VBT)—e.g., in the form ofhistograms of each BC and BT for the entire vascular tree or withinselect ROI(s), with the ability to view such variability for a singlevessel or a group of vessels on the whole tree or within select ROI(s),or color encoded regions within a vascular tree/ROI (e.g., color encodedchips a Poker Chip representation) based on BC or BT values; or anycombination of two or more thereof. Distributions of one or more ofthese characteristics, or combinations of characteristics, or relatedstructural changes over time, may be identified as structural patternsthat can be associated with one or more conditions of interest.

Blood vessels may be binned according to about any of the followingnon-limiting diameter ranges (in microns): 0-10, 10-25, 25-50, 50-75,75-100, 100-150, 150-200, 200-300, 300-400, 400-500, 500-1,000, or anycombination thereof However, any other suitable bin size ranges(including larger, smaller, or intermediate) may be used. In someembodiments, the number of different bins may be between about 2 andabout 10. However, higher numbers of bins also may be used. In someembodiments, only 2 to 5 bins are used (e.g., 2, 3, 4, or 5). Forexample, three blood vessel bin sizes may be used: small, medium, andlarge diameters (e.g., small at less than about 35 microns or about20-35 microns, medium about 35-70 or about 35-100 microns, and largeabove about 100 microns or about 100-200 microns). However, other vesselsize ranges may be used to calculate population percentages or ratios asdescribed herein. In some embodiments, a single bin is chosen with apredetermined size range and no other sizes are analyzed.

In some embodiments, a parameter may be evaluated as a percentage of thetotal population of vessels. For example, the percentage of bloodvessels having a particular diameter (e.g., 20-40 microns) as apercentage of the total population of blood vessels may be used. In someembodiments, a parameter may be evaluated as a ratio of twosubpopulations within a population of vessels. It should be appreciatedthat the percentage populations of vessels having different propertiesmay be evaluated by determining the relative lengths of blood vesselshaving different properties within a region being analyzed. However,other techniques may be used.

Aspects of the invention relate to business methods that may involve themarketing and/or licensing of biomarkers associated with particularbiological processes, conditions, and/or diseases. In some embodiments,patterns (e.g., geometric features) of blood vessels (e.g., observed invivo or in casts) are analyzed to identify or evaluate associations orcorrelations with certain biological processes, conditions, and/ordiseases of interest. Pattern parameters may be identified that can beused as structural biomarkers (e.g., for clinical, diagnostic,therapeutic, and/or research applications as described herein). Thesebiomarkers may be used to reduce the cost and increase the efficiencyand sensitivity of medical and research techniques. In one embodiment,one or more biomarkers or methods of using the biomarkers may bemarketed to medical or research customers or potential customers. In oneembodiment, a fee-based service may be provided to medical or researchorganizations wherein information relating to a medical image isobtained and analyzed for the presence of one or more biomarkers and theresulting information is returned in exchange for a fee. The amount ofthe fee may be determined, at least in part, by the type of imageinformation that is provided, the type and degree of analysis that isrequested, and the format and timing of the analysis. It should beunderstood that aspects of the invention may be applicable to imageinformation obtained from one or more of many different scanningmodalities (including, but not limited to, micro CT, MDCT, rotationalangiography, MRI, PACS). This information may be received from manydifferent sources, including, but not limited to one or more of thefollowing: medical centers, large pharmaceutical companies (e.g., inassociation with pre-clinical evaluations or during clinical trials),CROs (for both pre-clinical and clinical analyses), medical laboratoriesand practices (e.g., scanning centers), hospitals, clinics, medicalcenters, small biotechnology companies (e.g., in association withpre-clinical evaluations or during clinical trials), and bio-medicalresearch organizations. The results of the analysis then may be returnedto any one of these organizations. In some embodiments, the analysisresults may be returned to the same entity that sent the imageinformation. In other embodiments, the results may be returned to adifferent entity (e.g., the image information may be received from ascanning laboratory and the analysis may be returned to a physician).One or more steps involved with receiving the information, analyzing thestructural features, processing the results and forwarding the resultsto a recipient may be automated. It also should be appreciated that oneor more of these steps may be performed outside the United States ofAmerica. Business procedures (e.g., marketing, selling, licensing) maybe performed individually or collaboratively.

Aspects of the invention may be described herein in the context ofindividual analytical steps, particular structural features, etc.However, it should be appreciated that any of the methods and devicesdescribed herein also may be incorporated into a business methodassociated with the use of a biomarker based on one or more blood vesselstructural features or patterns (e.g., structural features or changesobserved in vascular casts obtained from therapeutic and/or diseasemodels or conditions).

Aspects of the invention may be automated (e.g., using one or morecomputer-implemented acts described herein). It should be appreciatedthat one or more pattern parameters (e.g., individual blood vesselstructural feature(s), distributions of blood vessels or blood vesselstructural features, or combinations thereof) may be analyzed using oneor more quantitative and/or qualitative methods (e.g., based on binneddata). In some embodiments, one or more parameters may be measured andquantified and the measurements may be analyzed using standardquantitative and/or statistical techniques for evaluation and/orcomparison with threshold or reference values as described herein. Incertain embodiments, one or more parameters may be evaluated using apredetermined scoring method, for example based on predetermined factors(e.g., for binned data). Geometrical parameters may be represented usingvectors. For example, a distribution of blood vessels, blood vesselcurvatures, blood vessel tortuosity, or blood vessel directions within avolume of interest may be represented using a plurality of vectors.Separate vectors may be used to represent separate vessels (e.g.,vessels for which a connectivity has not been determined during theanalysis). However, separate vectors also may be used to representindividual segments or fragments of a single blood vessel or portion ofa vascular tree (e.g., for which connectivity has been or may bedetermined during the analysis). Vasculature pattern parameters may beanalyzed using any appropriate technique for separating and/orcategorizing numerical values or scores.

In some embodiments, a score may be obtained to relate a patternparameter to the probability of a physiological condition such as adisease or disease stage. Aspects of the invention can be used for insitu diagnostic, interventional and therapeutic analysis of one or moredisease loci associated with aberrant internal structures. As usedherein “in situ” means in an animal (e.g., a human) body as opposed toin a biopsy or other tissue sample. Aspects of the invention can be usedto research structural changes associated with a disease, for developingand evaluating disease treatments including therapeutic drugs, and forother purposes. Aspects of the invention include automatically analyzinga structural feature or pattern and automatically generating a scorebased on the analysis.

In some embodiments, aspects of the invention include detecting and/oranalyzing selected internal tubular networks in situ in animals and/orin vascular casts. As used herein, an internal tubular network means anetwork of connected cylindrical internal body structures. Tubularnetworks include, but are not limited to, cardio-vascular, respiratory,gastro-intestinal, and genito-urinary systems and portions thereofwithin animal bodies. Accordingly, the cylindrical structures mayinclude branched, straight, curved, and/or twisted cylindrical elements.The cylindrical structures and elements may include not only cylinders,but also may include flattened or otherwise distorted regions. Thecross-section of a cylindrical structure or element may be circular,oval, approximately circular, approximately oval, or more irregular innature. The internal diameter of the cylindrical elements may vary ormay be approximately the same over the region of interest. A tubularnetwork such as a circulatory network may be closed off from theenvironment outside the animal. In contrast, tubular networks such asrespiratory and gastro-intestinal networks may be open to the outsideenvironment. In some embodiments, appropriate casting and/or contrastagents (e.g., inhaled agents) may be used to analyze respiratory and/orgastro-intestinal networks.

In one embodiment, aspects of the invention include analyzing arepresentation of a tubular network (e.g., a mathematical representationof a vascular network). In one embodiment, a representation of anetwork, or a portion thereof, may be obtained (e.g., from an existingdatabase or a remote site) and analyzed. In another embodiment, arepresentation of a network, or a portion thereof, may be generated fromstructural data and then analyzed. According to aspects of theinvention, an analysis may include detecting the presence or absence ofone or more structural features or patterns, measuring or evaluating theextent of one or more structural features or patterns, or a combinationthereof.

In one embodiment, aspects of the invention are useful for selectivelydetecting and/or analyzing patterns (e.g., structures) of an animal'svasculature to detect or monitor one or more blood vessel patterns(e.g., structures) that may be indicative of a physiological conditionof the animal. A structural pattern or feature may be detected and/oranalyzed for blood vessels of any size including, but not limited to,arteries, arterioles, veins, venules, and capillaries.

In one embodiment, aspects of the invention are useful for selectivelydetecting and/or analyzing structural features or patterns of ananimal's vasculature to detect or monitor one or more blood vesselstructures that are characteristic of disease (e.g., a diseaseassociated with angiogenesis). A blood vessel structure or patterncharacteristic of a disease (e.g., a disease associated withangiogenesis) may provide an early diagnostic indication of the presenceof the, which can allow for early treatment that can improve a patient'sprognosis. In other embodiments, a blood vessel structure or patterncharacteristic of a disease (e.g., a disease associated withangiogenesis) can be used as a marker (e.g., a biomarker) for stagingand/or grading, to monitor disease progression, evaluate a prescribedtherapy, and/or identify and/or validate a drug or treatment regimen forthe disease. Diseases associated with abnormal vasculature structures orpatterns include, but are not limited to, cancer, cardiovascular,dermatologic (skin), arthritic, musculoskeletal, central nervous system,neurologic, pulmonary, renal, gastrointestinal, gynecologic,genitourinary, inflammatory, infectious, and immunologic diseases.

A cancer may be a solid tumor or a leukemia. When the cancer is aleukemia, methods of the invention may be directed to detecting and/oranalyzing vasculature pattern(s) in the bone marrow of an animal (e.g.,human).

It also should be appreciated that aspects of the invention may includeperforming any combination of two or more acts described herein and thatcertain acts may be omitted in some embodiments. In one embodiment, thepresence of one or more structural abnormalities may be identified ordetected in a body region without generating and/or analyzing astructural representation of that body region. For example, the presenceof a blood vessel abnormality may be detected directly from structuredata for a body region without generating a structural representation ofthe vasculature for that entire body region. In another embodiment, ananalysis may involve selectively representing one or more abnormalstructures if they are present in a body region without representingnormal structures in that body region (e.g., abnormal blood vesselstructures may be represented without representing any normal bloodvessels, or without representing all the normal blood vessels, withoutrepresenting most of the normal blood vessels, etc.). In anotherembodiment, an abnormal vascular structure may be identified or detectedwithout obtaining a detailed representation of the all the blood vesselsin a body region. It may be sufficient to detect the presence of oroutline of a vascular tree in a body region and perform an analysis thatidentifies or detects abnormal structures on specific blood vessels orthe presence of excessive vascularization (e.g., a clump ofneovasculature representing malignancy) without representing all thenormal details of the vascular tree or even detecting individual bloodvessels in the vascular tree. Accordingly, in some aspects a lowresolution data set for a body region may be sufficient to detect oridentify certain structural indicia of a disease such as cancer.

Aspects of the invention may include automating one or more acts. Forexample, an analysis may be automated in order to generate an outputautomatically. Acts of the invention may be automate using, for example,a computer system.

As should be appreciated from the foregoing, in one embodiment, raw orprocessed structure data may be obtained at a medical or research centerand sent to a computer at a remote site where one or more of theanalytical steps described above may be performed (e.g., for a fee). Theoutput from the analysis may be then returned to the medical or researchcenter either in computer readable form to a computer at the medical orresearch center, in a hard copy, in another tangible form, or in anyother suitable form including those described herein.

In another embodiment, one or more software programs that implement oneor more functionalities described herein may be provided and installedat a medical or research center (e.g., for a fee). The programs can beprovided on disk, downloaded from an internal or remote (e.g., external)site, or loaded in any suitable manner. Reference information that isused in any functionality described herein may be provided along withthe software or separately. In one embodiment, reference information(e.g., information relating to normal or abnormal blood vesselstructures) may be available on disk, downloaded from an internal orremote (e.g., external) site, or loaded in any suitable manner.

As used herein, “remote” means at a site that is different from theimmediate location of the imaging device (e.g., the medical scanner).The remote site can be a central computer or computing facility at ahospital, medical, or research center (e.g., within the network orintranet of the center), or can be outside the hospital, medical, orresearch center (e.g., outside the network or intranet of the center).The remote site can be in the same state, in a different state, or in adifferent country from the site of data acquisition by the imagingdevice.

In some embodiments, multimodal analyses (e.g., using structure datafrom two or more different types of imaging devices) may be usedtogether. Accordingly, aspects of the present invention may include theability to process and analyze different types of structure data andeither combine the results to generate a combined output, or to generatea separate output is generated for each imaging modality. In someembodiments, an organ, tissue, or animal perfused with a casting agentand/or an imaging agent may be sent to an imaging center for analysis.

In some embodiments, in vivo and/or ex vivo casting methods of theinvention can be used to identify one or more vascular patterns (e.g.,including one or more structural parameters, structure distributions,combinations thereof) and/or time-dependent changes thereof that can beused as biomarker(s) for a disease or a response to a therapy, or formonitoring patients for indicia of disease or response to therapy, orfor other applications where vascular information may be informative.Accordingly, such vascular patterns or changes thereof identifiedaccording to methods of the invention can be used for diagnostic,interventional, therapeutic, research, and treatment development andevaluation. Non-limiting examples of some of these embodiments aredescribed below.

EXAMPLES Example 1 Xenotopic Tumor Models

A tumor model can be generated by inoculating human non-small cell lungtumor cell line (A549 from ATCC, Inc.) subcutaneously in immunodeficientmice (SCID). SCID male mice (6-8 weeks old from Charles River Inc.) areinoculated subcutaneously in the lower back with a suspension of 1×10⁶human lung tumor cells (A549) in 0.2 ml of PBS. All mice are fed normalchow diet throughout the duration of the experiment. All mice weightsare measured throughout the experiment. Tumor size is measured withcalipers twice-a-week and tumor volume is calculated using the formulaLength²×Width×0.52. All mice are randomized into two treatment groups(approximately 10 mice per group) when the median tumor volume reachesapproximately 500 mm³. The treatment groups can be treated according tothe following schedule using intraperitoneal (i.p.) administration ofeither a control composition or an anti-angiogenic compound. Forexample, different levels of an anti-angiogenic compound can be used andthe results compared to a control group that is not treated with ananti-angiogenic compound (e.g., Avastin® available from Genentech, SouthSan Francisco, Calif.). For example:

Group 1: Control group—treated with saline/PBS twice a week.

Group 2: High Avastin®—treated with Avastin® at 5 mg/kg/i.p. twice aweek.

Group 3: Low Avastin®—treated with Avastin® at 0.5 mg/kg/i.p. twice aweek.

Experiments are terminated 1.5 weeks after initial treatment.

At the end-point, all mice are anesthetized and systemically perfusedwith a casting agent.

Example 2 Perfusion with Casting Agent

Perfusion with a casting agent, Mercox (available from Ladd Research,Williston, Vt.) can be performed as follows. An initial anticoagulationstep for each animal is performed using an i.v. injection of heparin(10,000 U/ml, 0.3 cc/mouse). After 30 minutes, the animals areanesthetized. Each animal's heart is cannulated and the animal perfusedwith warm physiological saline at physiological pressure (with an openvein draining the organ or with an open vena cava). Perfusion iscontinued until the organ or animal is clear of blood. Mercox monomer isfiltered through a 0.5 μm filter and a casting resin is prepared bymixing 8 ml Mercox, 2 ml methylmethacrylate, and 0.3 ml catalyst. Theresin is infused through the same cannula until the onset ofpolymerization (the resin changes color to brown and emits heat, ˜10min). The organ or animal is carefully immersed in a 60° C. water bathfor 2 hours (or overnight in a sealed container). The tissue is removedby incubating in alternating rinses of 5% KOH and distilled water (forexample in a 60° C. water bath sealed) followed by thorough rinsing indistilled water. The cast is cleaned in 5% formic acid for 15 minutesand rinsed thoroughly in distilled water and frozen in distilled water.The resulting block of ice is lyophilized (care should be taken not tomelt the ice, the ice should melt as it lyophilizes). The resulting castcan be analyzed to identify one or more structural characteristics ofinterest.

Example 3 Xenotopic Tumor Models Response to Anti-Angiogenic Therapy

Xenotopic mouse models obtained as described in Example 1 were treatedwith either a control solution of saline/PBS or an anti-angiogenicpreparation of Avastin® at 0.5 mg/kg/i.p. as described above. At theend-point, vascular casts were prepared as described in Example 2 aboveand analyzed for two treated mice (both treated with Avastin® at 0.5mg/kg/i.p.) and one control mouse. The resulting vascular casts werescanned using a micro CT-scanner and the results of the structuralanalysis are shown in FIGS. 14-17. The analysis was performed bydetermining the number of blood vessels within bins of differentdiameter ranges for the xenotopic tumor in the treated and controlanimals. The bins were each 13.8 μm wide and the smallest bin includedblood vessels having a diameter of between 20.7 μm and 34.5 μm. Meantumor volumes did not differ significantly between the groups at the endof the experiment. However differences in blood vessel diameterdistributions were detected as shown in FIGS. 14-17. FIG. 14 shows theresulting vessel population distribution. Treated tumors had 20% lesssmall diameter sized vessels than untreated tumors, and treated tumorshad a higher percentage of middle diameter sized vessels than untreatedtumors. The blood vessel population distributions were consistent forboth treated animals. FIG. 15 shows the vessel population ratio betweensmall (approximately 21-35 μm) and middle (approximately 35-49 μm) sizevessels in the tumors of the control and treated animals. The ratiodecreased after inhibitor treatment with Avastin®, and this ratio wasconsistent within the treated group. FIG. 16 shows the vessel populationratio between large (approximately 147-161 μm) and middle (approximately33-77 μm) size vessels. The ratio decreased after treatment withAvastin®, and this ratio was consistent within the treated group.Additional experimental results are shown in FIGS. 17-19.

The following considerations apply to the specific examples and theentire written specification herein (including the summary, detaileddescription, and claims). It should be appreciated that casts, like insitu blood vessels, are three-dimensional structures. Accordingly,imaging and analytical techniques described herein provide informationabout three-dimensional structural characteristics. In some embodiments,techniques are used to generate three-dimensional representations ofvascular casts and/or in situ blood vessels. In some embodiments,techniques are used to generate three-dimensional images of vascularcasts and/or in situ blood vessels. The three-dimensionalrepresentations and/or images can be analyzed as described herein.

However, it should be appreciated that aspects of the invention are notlimited to three-dimensional structural characteristics. In someembodiments, aspects of vascular casts and/or in situ blood vessels maybe represented and/or imaged in one or two dimensions and an analysis ofone or two-dimensional features may be performed and used as describedherein. It also should be appreciated that the structural featuresdescribed herein may be measured or quantified using any appropriateunits, including numbers, lengths or distances, angles, percentages,etc., or any combination thereof, further including any of these unitsas a function of volume or area. Similarly, it should be appreciatedthat vascular changes over time or in response to treatment may involvean increase or a decrease of one or more of these structural features.For example, an increase in structures associated with angiogenesis maybe associated with certain disease progressions. In contrast, a decreasein structures associated with angiogenesis may be associated withdisease regression (e.g., in response to treatment).

It also should be appreciated that descriptions herein related toobtaining distributions of quantitative values for vessel parameterswithin a region of interest are preferably based on methodologies thatdetect and quantify all or substantially all of the detectable vesselswithin the region of interest based on the detection technique that isused for that analysis. Different techniques may have differentefficiencies. However, profiles and comparisons are preferably based ondata from the same or equivalent detection and/or reconstructiontechniques. It also should be appreciated that comparisons and/oranalyses described herein may involve a statistical analysis using oneor more standard statistical techniques to determine whether a change ina structure or pattern or other characteristic described herein (e.g.,an increase or decrease over time, or in response to a therapeuticdrug), or a difference or similarity between two structures or patternsor other characteristics described herein are statistically significant.

Having thus described several aspects of at least one embodiment of thisinvention, it is to be appreciated various alterations, modifications,and improvements will readily occur to those skilled in the art. Suchalterations, modifications, and improvements are intended to be withinthe spirit and scope of the invention. Any suitable analyticaltechniques may be used for perfused tissue and organs according to themethods described herein, including for example, the analyticaltechniques that are described in PCT US2005/047081 and PCT US2007/026048the disclosures of which are incorporated herein by reference in theirentirety. Accordingly, the foregoing description and embodiments are byway of example only. In the event of conflict between differentdisclosures, the disclosure of the present application shall control.

It should be appreciated from the foregoing, there are numerous aspectsof the present invention described herein that can be used independentlyof one another or in any combination. In particular, any of the hereindescribed operations may be employed in any of numerous combinations andprocedures. In addition, aspects of the invention can be used inconnection with a variety of types of images or any dimensionality.Moreover, one or more automatic operations can be used in combinationwith one or more manual operations, as the aspects of the invention arenot limited in this respect. Distribution analyses, however obtained,may be used to facilitate the characterization of any of variousmorphological changes to tissue and/or to assist in assessing theefficacy of treatment using any of the herein described techniques,alone or in combination.

The herein-described embodiments of the present invention can beimplemented in any of numerous ways. For example, the embodiments ofautomatic distribution analysis may be implemented using hardware,software or a combination thereof. When implemented in software, thesoftware code can be executed on any suitable processor or collection ofprocessors, whether provided in a single computer or distributed amongmultiple computers. It should be appreciated that any component orcollection of components that perform the functions described herein canbe generically considered as one or more controllers that control theherein-discussed functions. The one or more controllers can beimplemented in numerous ways, such as with dedicated hardware, or withgeneral purpose hardware (e.g., one or more processors) that isprogrammed using microcode or software to perform the functions recitedherein.

It should be appreciated that the various methods outlined herein may becoded as software that is executable on one or more processors thatemploy any one of a variety of operating systems or platforms.Additionally, such software may be written using any of a number ofsuitable programming languages and/or conventional programming orscripting tools, and also may be compiled as executable machine languagecode. It should be appreciated that one embodiment of the invention isdirected to a computer-readable medium or multiple computer-readablemedia (e.g., a computer memory, one or more floppy disks, compact disks,optical disks, magnetic tapes, etc.) encoded with one or more programsthat, when executed, on one or more computers or other processors,perform methods that implement the various embodiments of the inventiondiscussed herein. The computer-readable medium or media can betransportable, such that the program or programs stored thereon can beloaded onto one or more different computers or other processors toimplement various aspects of the present invention as discussed herein.It should be understood that the term “program” is used herein in ageneric sense to refer to any type of computer code or set ofinstructions that can be employed to program a computer or otherprocessor to implement various aspects of the present invention asdiscussed herein. Additionally, it should be appreciated that accordingto one aspect of this embodiment, one or more computer programs that,when executed, perform methods of the present invention need not resideon a single computer or processor, but may be distributed in a modularfashion amongst a number of different computers or processors toimplement various aspects of the present invention.

Use of ordinal terms such as “first”, “second”, “third”, etc., in theclaims to modify a claim element does not by itself connote anypriority, precedence, or order of one claim element over another or thetemporal order in which acts of a method are performed, but are usedmerely as labels to distinguish one claim element having a certain namefrom another element having a same name (but for use of the ordinalterm) to distinguish the claim elements. Also, the phraseology andterminology used herein is for the purpose of description and should notbe regarded as limiting. The use of “including,” “comprising,” or“having,” “containing”, “involving”, and variations thereof herein, ismeant to encompass the items listed thereafter and equivalents thereofas well as additional items.

What is claimed is:
 1. A method of detecting at least one featureassociated with a blood vessel in at least one image of at least oneblood vessel using a matched filter adapted to respond to the at leastone feature, the method comprising: applying a scale detection filter toselected voxels in the at least one image to determine a scale for thematched filter at each of the selected voxels; determining anorientation for the matched filter at each of the selected voxels,wherein determining the orientation is assisted by using the scaledetermined at each of the selected voxels; applying the matched filterat each of the selected voxels at the scale and the orientationdetermined at each of the selected voxels to obtain a filter response ateach of the selected voxels; and analyzing the filter response at eachof the selected voxels to determine if the respective voxel correspondsto the at least one feature.
 2. The method of claim 1, wherein the scaledetection filter is orientation independent.
 3. The method of claim 2,wherein the scale detection filter is symmetric with respect toorientation.
 4. The method of claim 3, wherein the scale detectionfilter includes a spherical kernel.
 5. The method of claim 1, whereindetermining orientation includes using a first derivative operator todetermine orientation.
 6. The method of claim 1, wherein analyzing thefilter response includes selecting voxels having a maximum filterresponse in a neighborhood to provide a plurality of centerline voxels.7. The method of claim 6, wherein the neighborhood size at each of theselected voxels is determined based on the scale determined at each ofthe selected voxels.
 8. The method of claim 6, further comprisingforming a geometrical representation of the at least one vessel, thegeometrical representation including a poker chip representation at eachof the centerline voxels, each poker chip representation having alocation of the centerline voxel, a radius of the vessel at thelocation, and a direction of the vessel at the location.
 9. The methodof claim 8, wherein, for each poker chip representation, the radius isdetermined based on the scale detected at the corresponding location andthe direction is determined based on the orientation detected at thecorresponding location.
 10. The method of claim 6, further comprisinglinking together adjacent centerline voxels.
 11. The method of claim 10,wherein linking together adjacent centerline voxels includes: selectinga target voxel from the plurality of centerline voxels; comparing thetarget voxel with each other centerline voxel in the plurality ofcenterline voxels within a predetermined neighborhood, wherein comparingincludes: determining a distance between the target voxel and each ofthe other centerline voxels; determining a difference between theorientation at the target voxel and the orientation at each of the otherplurality of centerline voxels; and determining a difference between thefilter response at the target voxel and the filter response at each ofthe other plurality of centerline voxels; and linking the target voxelwith one of the other centerline voxels based, at least in part, on thecomparison.
 12. The method of claim 1, wherein applying the matchedfilter at each of the selected voxels includes applying a matched filterhaving a kernel f_(s)(r,z), where${f_{s}\left( {r,z} \right)} = \left\{ \begin{matrix}1 & {r \leq {s\mspace{14mu}{and}\mspace{14mu} z} \leq {\sqrt{2}s}} \\0 & {s < r \leq {{\sigma(s)}\mspace{14mu}{and}\mspace{14mu} z} \leq {\sqrt{2}{\sigma(s)}}} \\{- w_{s}} & {r > {{\sigma(s)}\mspace{14mu}{or}\mspace{14mu} z} > {\sqrt{2}{\sigma(s)}}}\end{matrix} \right.$ and −w_(s) is a value based on the detected scales.
 13. A method of determining a scale at each of a plurality ofselected voxels in at least one image of at least one blood vessel, thescale at each of the plurality of selected voxels being determined usingan orientation independent scale detection filter having a filter sizedefined by a radius, wherein the scale is used to determine the size ofa matched filter adapted to respond to at least one feature associatedwith the at least one blood vessel, the method comprising: (A) selectinga target voxel from the plurality of selected voxels at which todetermine the scale; (B) setting the radius to a predetermined minimumvalue so that the filter size is at a predetermined minimum; (C)applying the orientation independent scale detection filter at thetarget voxel to obtain a filter response; (D) comparing the filterresponse with a predetermined criteria; (E) increasing the value of theradius of the orientation independent scale detection filter to increasethe filter size of the orientation independent scale detection filter ifthe filter response meets the predetermined criteria; (F) performingacts (A)-(F) with increased filter size if the filter response meets thepredetermined criteria; and (G) setting the scale based on the value ofthe radius of the orientation independent scale detection filter if thefilter response does not meet the predetermined criteria.
 14. The methodof claim 13, wherein the scale detection filter is orientationindependent.
 15. The method of claim 14, wherein the scale detectionfilter is symmetric with respect to orientation.
 16. The method of claim15, wherein the scale detection filter includes a spherical kernel.